The Phrase "No Evidence" Is A Red Flag For Bad Science Communication

Is there "no evidence" that using a parachute helps prevent injuries when jumping out of planes? This was the conclusion of a cute paper in the BMJ, which pointed out that as far as they could tell, nobody had ever done a study proving parachutes helped. Their point was that "evidence" isn't the same thing as "peer-reviewed journal articles". So maybe we should stop demanding journal articles, and accept informal evidence as valid?

Is there "no evidence" for alien abductions? There are hundreds of people who say they've been abducted by aliens! By legal standards, hundreds of eyewitnesses is great evidence! If a hundred people say that Bob stabbed them, Bob is a serial stabber - or, even if you thought all hundred witnesses were lying, you certainly wouldn't say the prosecution had “no evidence”! When we say "no evidence" here, we mean "no really strong evidence from scientists, worthy of a peer-reviewed journal article". But this is the opposite problem as with the parachutes - here we should stop accepting informal evidence, and demand more scientific rigor.

But how do you make the case that these are different and warrant different treatment to John Q. Public? Because you're basically saying that the anecdotes of regular people are of less value than the hunches of scientists. Do scientists have some epistemic privilege?

Obviously, they do. But John Q. Public is going to find that insulting and bad faith actors like all of Fox News is going to characterize scientists as liberal, technological elites that claim to know better than good ol' hard workin' Americans. That it is true is inconsequential.