Steve,
Your reasoning is incorrect. A Club applies for hosting an event and offers one (or more) of its courses for this privilege. We just saw an example of that with the U.S. Open. It was awarded to Bethpage State Park for play on its Black Course.
Not that it was or wasn't Winged Foot, but the club itself could offer itself for play and specify which of its courses should be used...
In other words, it could be a single-course golf club or multiple-course club...
Sorry, as I won't reveal it either at this point...