When people do Bayesian reasoning as in this post, it seems like they always leave out the base rate, and I don't think that's legitimate. I would argue that the baseline P(evidence) for this is pretty high, which weakens any conclusions you might want to draw. Granted, you addressed that indirectly by saying you weren't going into the debate about whether the observations are really that mysterious, but when you were explicitly going through the factors in Bayes' theorem you completely skipped the denominator. I guess people ignore it because it doesn't change when you are comparing different explanations for the same evidence, but you're not really doing that.