The corollary also shows the limitations: you can't actually come up with a real probability for being wrong without knowing other things about this distributio

The corollary also shows the limitations: you can't actually come up with a real probability for being wrong without knowing other things about this distribution (you can't know how likely you are to be in the most populous time in the history of the human race without knowing the entire past and future history). So the whole argument from statistics holds no water: it depends entirely on other arguments that give a shape to the distribution, and those arguments have their own problems and ways that they can be attacked.