Noah Smith wants to challenge your silly preconceptions about your invincibility. Good on him. His job would have been a lot easier though if he'd have taken the simple step of decomposing his denominator.
So far so good. But note that the denominator isn't very illuminating.
A better way of stating the case:
Look at what this formulation does. It obliges you to calculate the relative probability of Type I and Type II errors. This expanded version explicitly forces you to consider the quality of evidence, both for and against.
Of course, Noah's critique of unknown (unknowable?) alternative hypotheses remains salient. Mankind's persistent epistemological blind spot is non-ergodicity. There will always be missing terms in that denominator.
But we do the best we can with what we've got.