Well, they’re talking about archeological data that itself includes evidence of the strike(s).
I don’t doubt that they can get pretty accurate estimates of the date from archaeology, or that the Chinese made records of comets appearing. But can they be sure that Native American oral traditions are genuine memories of the same events? It may be like Schliemann finding “Priam’s treasure” at Troy (now in Moscow) or the death mask of Agamemnon at Mycenae (in both cases the objects he found were centuries too early to have anything to do with the leaders at the time of the Trojan War). There could be some wishful thinking involved.