They dug their own hole (and they keep digging).
E.g. conspiracy theorists were spouting "China designed this virus" on Twitter from the beginning, but I never took those claims seriously (I mean, it's technically possible, but I'm 100% certain that anyone claiming this has absolutely 0 proof of it and are just saying it to stir shit up); on the other hand, government suppression of "lab leak" theory (and intentionally conflating it with the crazy "lab designed" theory) was extremely concerning.
The reason I object to the false equivalence between the two is that it helps legitimize the conspiracy nuts, which is worse all things being equal, regardless of mistakes made by institutions.
My argument is that by holding ourselves to a higher standard that eventually these morons selling magical promises will be left exposed as liars to 90%+ of people.
It's not easy, the biggest problem (imo) at the moment is that when these groups latch onto a small fact and spin lies most people are branding the small fact as misinformation of wrong other than accepting a common ground. This is dangerous and erodes the position of having sane intercourse.
Calmly explaining why people are wrong and explaining the reasoning behind this is always better imo than simply slapping someone down as happens all to often.
Not meaning to sound like I'm disagreeing, just trying to explain my position.
I'm probably wrong, I normally am about something, and I've probably gone counter to published papers on human nature but this is my 2 pence based on science outreach and seeing it done right and wrong.
Now that's out the way...
Unfortunately I'm talking about people's emotions and their decision to trust a source of information. This is clearly NOT a purely logical situation.
There is a false expectation that govt groups are always correct and don't admit mistakes,even if they were correct as they could be at the time. Failure to own these mistakes publically and discuss the shortcomings and failings puts you into the same level of distrust as a scientist view's a snake oil salesman.
I take part on science outreach and one of the most damming things is having to explain when some media celebrity scientist said something utterly stupid and not correct. You then get the envetable "who can i trust" argument and the best way to resolve that is to share more information in a respectable slow and distant way...
Aka actually educating people.