That's a fair point, but I'm not sure I understand the gist of the author's confusion. Any response I would craft would end up being a re-statement of the usual

That's a fair point, but I'm not sure I understand the gist of the author's confusion. Any response I would craft would end up being a re-statement of the usual one sentence definition of p-values and Bayesian probability, both of which are already under discussion elsewhere in the comments.