If someone is (or seems like they might be) privileging the hypothesis, it seems reasonable to say that the burden of proof is on them, not just as a social norm but also as a question of epistemology.

In other words, if there are a hundred boxes where the diamond could be and I claim that it's in box number 27, then it's reasonable that I ought to provide some evidence for this claim, rather than requiring the other person to come up with a hypothesis for why my claim would be false. There are an infinite number of false hypotheses, and if we try to test them all rather than focusing on the most promising ones, we'll never get anywhere.