Sorry but you don't need to go through a single school get your Sport ticket or even Private ticket. In fact most people don't go anywhere near a school to get a sport or private tickets, that's just if you want to accelerate the process or just need that extra re-assurance. They simply rent a plane and hire a CFI, read some books, take a written then practical test, done deal. Typically after sport or private one will seek out a school for further ratings after that level. The AMA could only wish they could propose such a successfully running program to get new, not as rich and health restricted pilots either up, or back up, in the air.