Multiple witnesses, fresh crater where they described the impact. They reported a phenomenon that conflicted with everything they knew about the perfection on the heavens. No reason to lie, and every reason to reject what they saw. What's to doubt?
[two years later] The doubt was cast by someone doing his doctoral work; he claims that, if there had been such an impact (the impact crater was identified a while ago), there should have been massive numbers of shooting stars reported. IOW, to take this criticism seriously, one has to assume that this lone researcher was able, in a matter of weeks or months, to comb through all medieval manuscripts (reading them in the original language); also, one has to assume that his assertion is correct -- which means he figured out, based on a brief account from 800+ years ago, the exact velocity and character of the impactor.
IMHO, the doubter is full of it.