Monty Hall is analogous in that we are looking at evidence and trying to make conclusions about likelihoods. It is relevant because the likelihoods are different depending on what was in Monty's head in the past, after observing the same physical evidence. Monty is not the experimenter; where does that make a difference? Could one reformulate it so that he was? He would be running two different experiments, surely - but then why isn't that the case for the two researchers?