I assume that people in their pre-bayesian days aren't even aware of the existence of the sequences so I don't think they can use that to calculate their estimate. What I meant to get at is that it's easy to be really certain a belief is false if it it's intuitively wrong (but not wrong in reality) and the inferential distance is large. I think it's a general bias that people are disproportionately certain about beliefs at large inferential distances, but I don't think that bias has a name.

(Not to mention that people are really bad at estimating inferential distance in the first place!)