In England and Scotland at the very exclusive Clubs the process of picking the right visitor ia rather a dark and mysterious system. Suffice to say that if you are an average Joe in the UK you have no chance of playing Muirfield and many others (especially the Clubs around London and the Southeast).
I'm afraid that statement is, quite simply, utter nonsense. So long as you are a member of a club (any club, it can be a poxy £10 pay per play municipal) and have a handicap of 18 or better then you can book a tee time at Muirfield. I used to belong to just such a public course (Rickmansworth) where I had to queue at 6am each Sunday to book a tee time for the next weekend and the facilities were, shall we say, basic. That didn't stop me booking tee times and playing (and being welcomed) at Prestwick and Dornoch.
It doesn't help the debate to suggest some "dark and mysterious" skullduggery where none exists.