> This is extremely ordinary 'evidence'

Claims don't require special evidence whether they are extraordinary or not. "Extraordinary" claims can be proved with the same kind of evidence as other kinds of claims. Relativity was first tested by taking pictures of an eclipse, pretty pedestrian evidence relative to the cosmic scale of it's implications.

What is true is that, the higher the confidence of your prior belief, the less impact new evidence will have. So extraordinary claims simply require more evidence, because our prior is that they aren't true with fairly high confidence.