There are indeed natural problems outside of NP, but an AI will be able to quickly answer any such queries in a way that, to a lesser intelligence, looks indistinguishable from an oracle's answers.

How do you know that? What makes you reach that conclusion?

Do you mean an AI that has already FOOMed? If so, this is sort of a trivial claim.

If you are talking about a pre-FOOM AI then I don't see why you think this is such an obvious conclusion. And the issue at hand is precisely what the AI could do leading up to and during FOOM.