Yes, people forget that the core to Fischer's approach was to start with a hypothesis, a plausible mechanism which would cause (or at least explain) the outcome

Yes, people forget that the core to Fischer's approach was to start with a hypothesis, a plausible mechanism which would cause (or at least explain) the outcome. Only then is it fair to use a p-value to show that your measurement is "something that wouldn't happen by random chance very often." As validation of a hypothesis which has merit on its own.