In this paper of Aaronson's, a proof is given of Occam's razor by appealing to PAC learning. My understanding of Valiant's bounds for PAC learners is that it requires i.i.d.

This is often a reasonable assumption to make. However, he used this proof of Occam's razor to justify the problem of induction (i.e. claim that the future will represent the past).

If you assume that the future and past data are drawn from the same distribution (which is how I think i.i.d. is being used), this strikes me as essentially assuming that the future will be similar to the past, so using PAC learning here begs the question.

Am I misunderstanding the use of i.i.d.? Is there a way around this problem?