Broussard makes a bit of a dog's breakfast out of what is actually a fairly straightforward subject. Hume had it right in what the modern Bayesian recognizes as being the precisely correct way: a hypothesis with low prior probability has to be supported by evidence which would be more improbable were the hypothesis false.
Broussard's examples all either ignore major relevant evidence or make Hume's argument a strawman (or both). Why do we believe that the Big Bang happened? We have evidence that not only would be vastly improbable had it not happened, but which was predicted in advance from theory, which eliminates a whole class of post-hoc justification biases. We don't say that scientific laws can't be revised, because the revised laws must not be inconsistent with the previously established evidence, while new evidence may be inconsistent with the old laws. Hume never said that merely being rare would make it impossible to believe in some event; indeed, he gives examples of the kind of evidence that would justify belief even in highly unlikely propositions.
So Broussard's claim that Hume is setting too high a bar is completely unjustified, and the modern Bayesian knows (as Hume did not) that this can be justified mathematically.
And then the whole thing degenerates into farce when Broussard claims that human activities such as lying or stealing bodies are somehow more improbable than an actual resurrection of a dead person. And the argumentum ad martyrdom is ridiculous: we have no good reason to believe that any church figure from the 1st century was martyred at all, and we especially do not have any reason to believe that of any actual disciple of Jesus.