Lately I've been reading some hard-core Calvinists. And I've noticed that they are coming across the same issue: what makes these "pastors" qualified to lead? There was an article recently with a title like "So you want to make a living at this business?" criticizing "pastors" as simply fellow church members and suggesting they make their livings as tent-makers the way St. Paul did.
The upshot of this way of thinking appears to me to be a trend towards "home church." They are rejecting the authority of the Church entirely. And I see this reflected on both sides of the divide, both from those who are staying home with their families on Sundays, and from those (Andrew Sandlin, Gary North come to mind) who are criticizing and opposing the anti-institutional trend.
I guess my point is that the issue of "By what authority?" is not being asked entirely from the outside, but is a hot-button issue right now internally within the Presbyterean fellowship and I assume within other denominations as well. Actually, these guys despise Baptists, and they especially despise the "profit oriented" preachers giving a Gospel of wealth and success. So if they have problems with authority in their own sect, they utterly reject the authority of most of their fellow protestant pastors.
I am not familiar with Sandlin, I am familiar with Gary North. I do not consider him mainstream Calvinism. In His book Unholy Spirits he endorsed Robert Tilton (who is a fruitcake). His Y2K hysteria (a regular on Art Bell at the time) was embarassing.
The home church movement is unbiblical. I have no problem meeting in a home but the family and the church are not interchangeable.
OP can speak to the issue within Presbyterianism. I am a credo baptist, non-denominational type. I do denounce Health and Wealth Prosperity preachers (which includes North's bud -- Robert Tilton). BTW, in Unholy Spirits North says that prosperity theology is embraced some theonomic principles.