Here is a dialogue to help 
further illustrate the fact that in a Presbyterian system of church government, denominational division implies a refusal to acknowledge each others' 
de jure legitimacy and authority as churches.
The dialogue is entirely fictional.  It is between Frank and an "OPC Elder."  The elder represents no particular person.  I chose the OPC because I am familiar with it and know where to find things quickly in its Book of Church Order, and not because the OPC suffers from semi-congregationalism more than other modern Reformed denominations (the disease is quite widespread both in America and abroad).  In past hypothetical examples and conversations, I have used the PCA, the RCUS, etc.
Frank: 
 There is a PCA church about an hour away from here.  Do you consider 
its session, and the officers that make up its session, to have full 
de jure authority?
OPC Elder:  Yes, I do.
Frank:  Just as full and real as your authority and the authority of your own church session?
Elder:  Yes.
Frank: 
 The Book of Church Order of the OPC affirms Presbyterian church 
government as biblical.  In Presbyterian government, there are a limited
 number of authoritative offices in the church.  There are ruling 
elders, teaching elders (which can include ministers as well as 
theological doctors), and deacons.  Am I correct?
Elder:  Yes, that is correct.
Frank:  Are there any other offices recognized by the church?
Elder:  No.
Frank:  The elders (both teaching and ruling) have responsibility for governing the church, correct?
Elder:  Yes.
Frank:  Are the governing officers to function independently, or together as a board of elders?
Elder: 
 They are to function together and exercise their authority together.  
The board of elders is called the "session."  The session as a whole has
 more power than individual officers alone, and it can act as a court 
overseeing not only church members but individual officers who are part 
of the session.
Frank:  The OPC's Book of Church Order (
Chapter XII, "Governing Assemblies")
 describes how the church is to function corporately, with individual 
officers functioning together as sessions, and sessions being parts of 
larger governing bodies such as presbyteries, general assemblies, etc.:
Each governing assembly exercises exclusive original jurisdiction over 
all matters belonging to it. The session exercises jurisdiction over the
 local church; the presbytery over what is common to the ministers, 
sessions, and the church within a prescribed region; and the general 
assembly over such matters as concern the whole church. Disputed matters
 of doctrine and discipline may be referred to a higher governing 
assembly. The lower assemblies are subject to the review and control of 
higher assemblies, in regular graduation. These assemblies are not 
separate and independent, but they have a mutual relation and every act 
of jurisdiction is the act of the whole church performed by it through 
the appropriate body.
Do you agree with this portrayal of how church officers and courts are to function?
Elder:  Yes.  This is basic Presbyterianism.
Frank: 
 It would seem to me that this system of things implies that each 
individual officer has a right and a duty to function as a member of a 
session, and that sessions have a right and a duty to invite and require
 that individual officers functioning in their congregations function as
 parts of the session.  Likewise, it would seem that each individual 
session has a right and a duty to function as a member of a larger 
regional body (a presbytery), each presbytery has a right and a duty to 
function as a part of a larger general assembly, and so on, and that the
 larger assemblies have a right and a duty to invite and require the 
lower assemblies to function as members of these higher assemblies.  Am I
 correct in these observations?
Elder:  Yes, quite correct.
Frank:  Is your session a part of a larger regional church?
Elder:  Yes, we are part of the Presbytery of New York and New England.
Frank: 
 Judging from all that has been said, I presume that the PCA church an 
hour from here, as it is recognized as having full legitimacy and 
authority as a church session, is regularly invited to participate as a 
member church of the Presbytery of New York and New England.  Am I 
correct?
Elder:  No, that is not the case.  Although we
 would welcome the PCA church to bring fraternal greetings to the 
presbytery meeting, the officers of that church are not allowed to 
function as voting members of the presbytery.
Frank:  Why not?
Elder:  We are separate denominations.
Frank:  What does that mean?
Elder: 
 We don't have a fully worked-out, mutually agreed-upon set of standards
 for doctrine and practice (though we are close), and we function 
independently from each other.  We are not united under common binding 
councils.
Frank:  How can you function independently of 
each other?  According to the OPC's Book of Church Order, which I quoted
 a few moments ago, individual church courts never function 
independently from each other:  "These assemblies are not 
separate and independent, but they have a mutual relation and every act 
of jurisdiction is the act of the whole church performed by it through 
the appropriate body."  It seems to me it is very un-Presbyterian to 
have church courts functioning independently from each other, with no 
possibility of appeals to higher mutually-binding assemblies, etc.
Elder: 
 Well, we don't agree on all matters of doctrine and practice, and 
concern for the purity of the church demands that we be careful about 
whom we unite with.
Frank:  No doubt that is the case.  
But you miss my point.  According to Presbyterian church government, as 
articulated in the OPC Book of Church Order, lower assemblies have a 
right and a duty to participate as members of higher assemblies, and 
higher assemblies have a right and a duty to invite and require lower 
assemblies to participate as members of themselves.  According to this 
system, which you acknowledge to be right and biblical, it would seem 
that by not inviting a fully legitimate and authoritative church session
 (such as you have acknowledged the PCA church an hour from here to 
have) to be a full member of presbytery, your presbytery is violating 
its duty as well as the rights of that church session.  And how can this
 be justified?
Elder:  You don't understand.  What you say is the 
ideal,
 but the church is not in an ideal state.  You can't expect the church 
to function according to ideal standards in non-ideal times and 
circumstances.
Frank:  Do non-ideal circumstances justify the breach of duty, or allow the claims of legitimate rights to be ignored?
Elder: 
 No, of course not.  But sometimes non-ideal circumstances necessitate 
that what would be considered a right or a duty in normal circumstances 
not be considered a right or a duty in the currently-prevailing 
circumstances.
Frank:  Are you saying that there are some 
situations that make it so it is appropriate for church courts to 
function independently, and that lower assemblies not be united under 
higher assemblies?
Elder:  Yes, I suppose that is what I am saying.
Frank: 
 In other words, there are circumstances--such as ones existing today 
(and for the past few hundred years at least), presumably--in which the 
church ought not to function under a Presbyterian form of church 
government?
Elder:  I didn't say that!  We must always 
be Presbyterian, but our Presbyterianism doesn't always manifest itself 
in the same ways.
Frank:  Well, Presbyterianism requires 
lower assemblies to be subject to higher ones, so it would seem that you
 are indeed justifying a not-fully-Presbyterian practice of church 
government.  If Presbyterianism is the biblical form of church 
government, how do non-ideal circumstances justify changing it?  I 
presume that you would not think it a good argument were I to justify 
bringing unbiblical practices, such as the use of images, into the 
church on the grounds that "current circumstances call for non-ideal 
practice."
Elder:  No, we can't ignore the teaching of the Word of God because of "non-ideal circumstances."  That is no excuse.
Frank: 
 I agree.  So why the exception when it comes to Presbyterian church 
government?  Why, in this case, do "current circumstances" imply that we
 should cease to follow biblical patterns of church government?
Elder: 
 Well, the Bible also says that we have a duty to preserve the purity of
 the church.  We are concerned that uniting with the PCA may dilute that
 purity, and we cannot unite with them until our concerns are assuaged. 
 Just as we should not ordain officers, especially teaching elders, 
until we are assured that they are biblically qualified and sound in 
doctrine and practice, so we cannot unite with any other denomination 
until these same sorts of conditions are met.
Frank:  I
 grant that the Bible commands the church to preserve her purity as well
 as her unity.  I grant that this is a good reason not to ordain certain
 men to the ministry of the church.  I also grant that this can be a 
good reason to refrain, at times, from uniting with another 
denomination.  However, concern for the purity of the church does not 
allow the church to ignore proper procedures of church discipline in 
dealing with existing church officers and courts.  For example, if the 
presbytery were to decide that your session was involved in serious 
doctrinal error, you would expect them to have to prove that and follow 
proper formal procedures in charging your session with errors.  They 
could not simply stop inviting you to presbytery meetings, etc.  And you
 should have the right to defend yourself against their charges in a 
formal way, and the right to appeal to a higher court should the 
presbyterial court decide against you.  Correct?  And if you should 
lose, and assuming the presbytery's case against you was just, your 
session would rightly be stripped of authority to function as a church 
session, right?  You would lose authority and legitimacy as a church 
session?
Elder:  Yes, all that is correct.
Frank: 
 Well then, since you have granted that the PCA session an hour from 
here is indeed a fully legitimate session possessing authority, I 
presume you will grant that the same process ought to be followed in 
their case as well?
Elder:  No.
Frank:  Why not?  Why don't they get to be treated the same as you?
Elder:  They are of a different denomination.
Frank:  Are they a legitimate and authoritative church session or not?
Elder:  They are.
Frank:  Then what does it even mean to say they are "of a different denomination"?  The phrase has no meaning to me.  They either 
are a fully legitimate church session, or they 
are not.  You have said that they 
are,
 so I don't see why they should be treated any differently from you or 
have any different rights or responsibilities relative to the rest of 
the church and to higher assemblies of the church.  I don't see how the 
statement that they are "of a different denomination" affects that at 
all or even adds any meaningful substance to the conversation.  Are you 
inventing new offices in the church of Christ?  For example, there are 
OPC elders, and these officers have different rights and 
responsibilities from PCA elders?  Where in Scripture (or in the OPC 
Book of Church Order) do we see distinct offices along these lines?
Elder:  We don't.  It's just that . . . well, they don't have the same status.
Frank: 
 What do you mean?  Are you saying that PCA elders have the same office 
as OPC elders, but they are not given permission to fully execute their 
roles for some reason?  Why would they not be allowed to execute their 
roles?
Elder:  They may not be fully orthodox in doctrine or practice.
Frank:  They 
may
 not be fully orthodox?  I wonder what you would do if the presbytery 
were to cease to invite you to presbytery meetings or give you or your 
elders any role in higher assemblies on the grounds (without any specifics mentioned) that you 
may or 
might
 not be fully orthodox?  To do this would be to discipline you, and that
 would require a full formal process, would it not?  It could not be 
done on a mere whim and the expression of some people's informal 
opinions?  Wouldn't they need to formally charge you with some 
particular error, etc.?
Elder:  Yes, that is correct.
Frank: 
 And what would happen if they were successful in charging you with 
something--say, that you are allowing unbiblical elements into worship?
Elder: 
 Assuming the charge held up after appeal to the general assembly, I and
 my session (if they went along with me) would have our authority as 
church officers and as a session revoked.
Frank:  Have the officers of that PCA church an hour from here had their authority revoked by such a formal process?
Elder:  No.
Frank:  Have any charges been brought against them?
Elder:  No.
Frank:  So why aren't they being invited as full voting members at presbytery meetings?
Elder:  Our presbytery can't charge them or revoke their authority, for they are not under our jurisdiction.
Frank:  Who's jurisdiction are they under?
Elder:  The PCA presbytery in the area.
Frank: 
 Well, if that presbytery is tolerating error in one of its sessions, 
you should appeal it to whatever assembly binds you both.
Elder:  There is no such assembly, because the PCA and the OPC are independent.
Frank: 
 But Presbyterianism requires churches to function inter-dependently 
under mutually-binding councils.  So how can two legitimate parts of the
 church be functioning independently?
Elder:  Well, we can't unite with them until we are sure they are fully orthodox . . .
Frank:  But if you have already accepted their full legitimacy and authority as a church, 
you have to function inter-dependently with them under mutual councils. 
 That is what Presbyterianism requires.  The only way you can avoid 
doing that is by refusing to recognize their 
de jure legitimacy 
and authority.  If you have recognized it in the past, you must 
repudiate it through proper formal channels (church courts, discipline 
cases, etc.).  If you have not recognized it in the past, then you can 
simply continue not to recognize it.  But what you can't do, in 
Presbyterianism, is acknowledge them as a legitimate part of the church 
(with all the rights and responsibilities that entails) and then treat 
them as if they are not.  But that is what you are doing.
Let me make a proposal as to how we should best understand your behavior:  In reality, you do not accept the 
de jure
 legitimacy and authority of that PCA church an hour from here.  You do 
not consider her officers (individually or collectively) as being 
subject to all the rights and responsibilities that 
de jure legitimacy entails.  You consider only OPC churches as truly, currently possessing 
de jure
 legitimacy and authority.  The problem is that you have become so 
confused by the culture and language of denominationalism that you can't
 see it or bring yourself to see it.  But if you want to continue to 
justly claim to be a proponent and practitioner of Presbyterian church 
government, you have no other choice.
UPDATE 6/24/14:  A second dialogue with a semi-congregationalist can be found 
here.