Of course. They'll lose trust the soonest when they see political statements coming out of the WHO, etc. And they should. An organization that can't stay neutral can't do good work in a politicized climate.
> Few can look at data and know what it doesn’t answer, or what questions should be asked but aren’t being
No, this is actually one of the easiest things to teach. "If you were paid to sneak in and ruin this team's research, what simple bias could you add? If it was the other way around, how would you protect against this?"
Teaching people to recognize a poorly controlled study is not difficult. But it's not PC these days because people are supposed to shut up when told that all scientists agree! We did this to ourselves a decade ago by tolerating the climate change debacle attacking dissent, now everything is fought through fake consensus.
> Correlation is not causation, but that escapes almost all of us
When it's not it almost always means there's an unseen factor though, so that wonderfully dismissive statement is usually just a red herring.
> The people who can (or do) communicate with the public are ...
Lying. They're lying. They're saying things they can't know as if they're fact. The WHO isn't saying that a lab leak seems less likely than other things, they're saying it didn't happen. Unless they can point to what did happen then logically they're not able to make that claim.
People might be scientifically illiterate, but luckily spotting lies is much easier and gets you mostly halfway there, able to spot when you're being manipulated even if you can't tell what the truth is. The real problem the media is having is that people aren't quite as dumb as expected.