I was musing on the old joke about anti-Occamian priors or anti-induction: 'why are they sure it's a good idea? Well, it's never worked before.' Obviously this is a bad idea for our kind of universe, but what kind of universe does it work in?

How can they possibly know/think that 'it' has never worked before? That assumes reliability of memory/data storage devices.

I don't see how these anti-Occamians can ever conclude that data storage is reliable.

If they believe data storage is reliable, they can infer whether or not data storage worked in the past. If it worked, then data storage is probably not reliable now. If it didn't work then it didn't record correct information about the past. In neither case is the data storage reliable.