You’re right, after rereading the proofs and talking with Evan, the only way for H to be polynomial time is to get oracle access to M. Which is slightly unintuitive, but makes sense because the part of the computation that depends on H and not on M is indeed polynomial time.
Yes, this says that humans can solve any problem in P. It says nothing about using M as an oracle.
It doesn’t talk about using M as an oracle, but otherwise I don’t see how the proofs pan out: for instance, how else is
supposed to only take polynomial time?
You’re right, after rereading the proofs and talking with Evan, the only way for H to be polynomial time is to get oracle access to M. Which is slightly unintuitive, but makes sense because the part of the computation that depends on H and not on M is indeed polynomial time.