Don't nuke it. Just a normal pushup. Chances are if they are yelling about that, they would have found something (as long as your pushups look good). If you want something to practice, I would say thumbs just touching your shoulders (if you go down to the deck) is about the widest you could go for a normal pushup.
As far as different standards for PFA and PT, if I'm interpreting the questions right that depends on the class. I had one DI that required perfect form all the time and another that would let you go to the deck on every pushup and struggle like an idiot with awful form (but he would beat the class until everyone looked like that, so it wasn't making things easier).