The NCAA can have whatever rules they want and say that it's voluntary members must not have ineligible players per their rules. School doesn't have to be an NCAA member.

Now based on what NCAA has said it doesn't appear it is going that way, but Kali can't control what the NCAA requires of its member institutions - they can control if the state sponsored Kali schools belong to the NCAA. They would be punishing the team/school not the paid player.