I didn't say they weren't.The NCAA is the schools. They aren't some separate body like a country club. The agreements are only as effective as the schools want them to be.
Ace Hardware is a cooperative of over 5,000 stores and 3,000+ individual store owners. The local owners own a share of the corporation. They do not have public stock or owners that are not owners of a store. That does not prevent the corporation from having rules that the stores must abide by.... created either by consensus or a representative board. There are mechanisms for removing stores from the cooperative or penalizing them for refusing.
It is nothing like a country club. It is a functioning and successful business model.