I’ve in general grown somewhat averse to the “burden of proof points in some direction” line of thinking.
They are both making claims. (And I think usually most people are making some sort of claim, unless they are just nitpicking). One is claiming that they remember a study — pretty vague, and easily proven (as far as we can tell at least) by just showing us any study. The other is claiming that that study doesn’t replicate… without having seen it, which seems like a pretty high bar to clear.