There is a very specific reason the visa laws for student pilots was introduced, it's called 9-11, that's how those f$)kers got their training.
You needed visas to enter the US well before 9/11. And the visa waiver program was always restricted to B-1/2 visas. Sure, they may have become stricter, but fundamentally 9/11 didn't change all that much as far as visas is concerned.
What did change was the whole TSA thing. With fingerprinting and everything. But that's not the discussion here. In fact, the flight school concerned clearly states that you have to do the TSA.