David -
You hit the nail on the head! Essentially, there are formal semi-private clubs, i.e. those cited in your example that advertise and promote themselves as both a private membership and daily fee course and then formal private clubs that allow the occasional unaccompanied guest to play their course through a variety of ways and means. In John's mind, any exclusive private club that allows unaccompanied guests to play, regardless of the number or frequency, is effectively semi-private club. I completely understand where he is coming from, though it's really stretching the definition of what constitutes a semi-private club in the U.S.
In one of the recent NLU "Strapped" videos, there's a scene where Big Randy is getting chastised by Soly and Tron for playing a semi-private club instead of a public course in the Northeast U.S. given the budget he and Neal (Schuster) had to stay within and doing so under the pretense they were to only play public courses. Randy's response to them was, "If a club is semi-private, doesn't that also mean it's semi-public?" I got a huge chuckle from that, because it's an accurate oxymoron.
Based on everything we've heard from John on this subject I believe in his mind that outside of the elite privates there are either semi-private or semi-public clubs/courses. Private clubs that allow unaccompanied guests fall into the semi-private category, while those that offer private membership and a daily fee rate are semi-public. I'm sure he'll correct me, but that's the gist I take from this.