There's a big difference. The membership of these classes is determined in the worst case - so if there is no polynomial time solution in the worst case then it

There's a big difference. The membership of these classes is determined in the worst case - so if there is no polynomial time solution in the worst case then it's NP. For this problem we don't care if it's possible that sometimes there are things that aren't verifiable, or the answers aren't exact, we just need training signal.