The point of that quote is of course not that the evidence must have some mythical flavor or whatever - that would be absurd, but rather that if your prior is a strongly held belief that something is not possible and thus the claim to the contrary is extraordinary, then the evidence sufficient to overturn that prior belief must naturally also be extraordinarily convincing.
It's just standard Bayesian reasoning (apologies if I'm misusing the terminology).
Given how much prior research has been done on superconductors, how attractive a target they are for research, and the demonstrated history of fraud in the field - it's not unnatural to retain skepticism concerning this story.
Doesn't mean the story is fraudulent or falsely believed to be fraudulent; it simply means that more evidence is needed to settle this convincingly. I'm sure will get that soon enough - either way.