I don't think establishing a corporation for liability purposes is going to invalidate the ability of the owners to fly and receive instruction in an airplane they provide. The FAR doesn't say they have to "own" the airplane, merely "provide" it.
The FAA is probably not interested in the exact financial mechanism as long as it is not an attempt to circumvent the rules. A one-airplane club with a handful of members, and new members approved by vote sounds very legit.
A large FBO-run for-profit "club" which calls it's renters "members" may run afoul of the reg. But there's a big grey area...my club is very large and the members consist of both owners who offer their airplanes for rent for profit, and non-owners who just "rent". Somehow they stay barely on the legal side and do not require 100 hours (we have been scrutinized 1001 times re. Mx). The lack of ownership on the part of most of the renters is not an obstacle, because they are part of the club which, collectively, arranges to have airplanes available for it's members. The fact that certain owner members can profit from this arrangement apparently does not invalidate the concept of the members collectively "providing" airplanes to themselves.