It seems like it is playing a little fast and loose with the interpretation of hypothesis, or maybe is mixing Bayesian and frequentist reasoning in the same exp

It seems like it is playing a little fast and loose with the interpretation of hypothesis, or maybe is mixing Bayesian and frequentist reasoning in the same experiment. Either way, something seems off about the logic here (regarding the madman thought experiment). it smells a bit like a case of equivocation, but i can't put my finger on exactly what it is (and in shrouded in a sheath of mathematics)