A Bayesian might argue that the basic assumptions that go into Bayesian epistemology (The assumptions for Cox's theorem + some assumptions that yield prior distributions) have the same status as the rules of logic - we conjecture that they're true and they stand up to criticism, ye we don't think we've proven these assumptions.

I don't think I have heard that argued. The problem of the reference machine in Occam's razor leads to a million slightly-different variations. That seems much more dubious than deduction does.