This is an oversimplification of “standards of evidence”. There are different standards of evidence between different fields. For example, I’m not sure there is 5 sigma statistical evidence that Pontius Pilate was a big shot in 1st century Palestine. Also, we have no repeatable experiments that can prove that Pilate existed. Yet the field of ancient history doesn’t operate with 5 sigma statistical evidence or lab experiments, so that’s OK.
But we cannot do the same with the claim that say, the Higgs boson exists. That sort of claim has to be established with the standards of particle physicists, which are an entirely different set of standards, which may have something in common with historians’ standards, but they’re not the same. They’re adapted in accordance with the nature of the object being studied. In this case, Higgs bosons are very different things compared with Roman prefects. So the standards are different. For example, discovering an old tablet that says “I saw the Higgs boson” would not be sufficient evidence for particle physicists to establish that the Higgs boson actually exists.
So coming back to the case of supernatural events, we have to first determine what supernatural events are, what they would look like, and what standards of evidence are appropriate to apply to them. As far as I can see, we don’t have an agreement on these questions, so we can’t proceed fruitfully on the question of their verification.