Does investigation actually "reveal some natural process at work," or is it just that if the investigator can dream up a plausible naturalistic explanation it's accepted without actual evidence?
No, the investigations do reveal truths and they are confirmed and that is how we know that they are truths.
Not to say that there isn't enough fraud in this arena to justify such dismissal in many cases, ...
It is the explanations that are dismissed and not necessarily the events.
I don't know why anybody would expect psychic phenomena to be produceable on demand, but since it isn't, that is made an excuse to dismiss the whole idea.
I agree that that is not a reasonable expectation and that some forces are sporadic. My question however, remains. Why is the whole idea more plausible than the employment of natural forces?