Dan,
The USGA and R&A don't own the game of golf, but the do own the Rules of the Game of Golf (see copyright statements).
As Tom said, anyone can come up with any rules they want and nobody will stop them. But, if they want a handicap or they want to play in a tournament run by most courses / associations / tours etc. they will have to play by their rules and most of the time, those rules are the ones written by the USGA / R&A.
When I go out to a course and get paired up with 3 other people and they find out what I do, they are frequently concerned that I will be a stickler on the rules with them. I say that as long as we don't have a bet or some other kind of competition going, they can do anything they please.
Ain't nobodies business by their own.