First of all, recall what Chapter 7 of the Second Book of Discipline of the Church of Scotland (1578) says about the various assemblies/courts of the church:
Assemblies are of four sorts. For, either are they of particular kirks and congregations, one or more, or of a province, or of a whole nation, or of all and diverse nations professing one Jesus Christ.Since the church of Christ is one throughout all the world, we have a set of concentric circles of church assemblies all the way from individual congregations through the ecumenical, general council of the whole church in all nations. All the members and officers of the entire catholic church are represented in this list. This is true presbyterian church government.
Now, contrast that with how Providence OPC's website describes the concentric circles of church courts:
In accordance to the general principles of the Bible (see Acts 15) and because no church officer or church court is above error or abuse, Presbyterianism is committed to mutual accountability between officers and local congregations. Consequently, there are various levels of church government arranged in graded courts, each of which contains a plurality of both Teaching and Ruling Elders, who are obligated to rule and be ruled according to the Word of God and to submit to one another in Christian love.Notice the significant difference here? Instead of having a series of ever-widening church courts going from the local congregation through to the entire catholic church, Providence OPC's view (so far as it appears from what is expressed here, at least) has the series of church courts go from the local congregation to the "denominational church."
As discussed above, "the local church" is overseen by "the Session," which is made up of at least one Minister/Teaching Elder and two Ruling Elders. . . .
In addition, each local congregation within a particular geographical boundary is part of a "regional church." This regional church is likewise overseen by a governing body known as "the Presbytery." Just like the Session of the local church, the Presbytery of the regional church is made up of both Teaching Elders/Ministers and Ruling Elders. . . .
Finally, all of the regional churches together make up the "denominational church" (in our case the Orthodox Presbyterian Church). And just like the local and regional churches, the denomination is overseen by a governing body known as "the General Assembly." This body is likewise made up of Teaching Elders/Ministers and Ruling Elders.
What in the world is the "denominational church"? I don't see any reference to such a thing in Scripture, or in any of the classic statements of presbyterian church government. I am reminded of David Campbell's recent article, in which he points out that the very concept of "denominationalism" is un-presbyterian. The idea of the final judicatory of the church being, not the ecumenical assembly of the whole catholic church, but rather some "denominational" assembly short of that is not presbyterian but rather semi-congregationalist in nature. The idea seems to be that the visible de jure catholic church consists of a number of separate and independent denominational conglomerations of churches which are not in full formal communion with each other under overarching binding councils. Thus, the OPC's highest judicatory is the "General Assembly" which is really just the "denominational church," and then there are all the other denominations with their supreme denominational judicatories--and all of this constitutes the worldwide de jure catholic visible church. I'm sure the leaders at Providence OPC would say that, ideally, the church ought to consist of only one worldwide church; but, so far as can be told from the language on this website, it appears they share the all-too-common-today tendency of Reformed churches to fail to understand the full implications of denominational disunity. That is, they seem to be sharing the fad of flirting with a semi-congregationalist rather than a purely presbyterian view of the nature of the visible church.
UPDATE 10/31/14: Here is a similar statement from Christ OPC in Salt Lake City, UT:
Though church government is often viewed as a matter of little significance, those who have spent much time in churches have generally found it is crucial. Hierarchical forms of government, whether the leaders be bishops or church bureaucrats, tend to sacrifice principle for pragmatism. Congregational forms of government offer no recourse outside the local congregation, so they turn disagreements into personal issues that easily split the church. They also can promote popularity at the expense of truth. Presbyterianism reflects biblical eldership: representative government and accountability.
The word Presbyterian simply comes from a transliteration of the Greek word for elder. Elders are elected from within the congregation who then serve as the ruling body of the church. There are teaching elders (pastors) and ruling elders; each has one vote. If someone has a complaint, it is to be taken to the local elders. If they do not yield satisfaction, the matter can be appealed to the presbytery, which consists of elders from churches within a geographic area. If the presbytery does not provide satisfaction, then the matter can be appealed to the general assembly, which consists of representative elders from all the churches in the denomination. We believe this is both Biblical and practical. Ideally, it avoids the problems inherent in hierarchical and congregational forms of government.
We see here, again, the semi-congregationalist attitude that puts the upper boundary of unity and mutual submission in the church at the level of the "denomination" instead of the entire catholic church.