Especially with covid it seems like social media has decided to counter propaganda rather than misinformation. I can see why, but I think it is wrong. Especially if the argument is 'this is false'.

To me, this shows once again that content moderation against misinformation does not fit with private parties.

That's what, at their best, most of the media are doing. Presenting well-researched, balanced, truthful stories, carefully selected to promote their own ideology. Forget journalism - this even happens in peer-reviewed science:

Ceci et al. (1985) found a similar pattern. Research proposals hypothesizing either "reverse discrimination" (i.e., against White males) or conventional discrimination (i.e., against ethnic minorities) were submitted to 150 Internal Review Boards. Everything else about the proposals was held constant. The "reverse discrimination" proposals were approved less often than the conventional discrimination proposals. - https://jsis.washington.edu/global/wp-content/uploads/sites/...

I think we need to work against the latter. I don't think censoring good-faith articles that are often abused is the way to do that.

I think BMJ has a pretty convincing reputation. So how can ANY fact checker flag an article from them without really good arguments?

Debates are all and good, but at some point, a decision has to be reached. Especially for a problem like the current pandemic, this unfortunately involves calls for every individual to radically change their behaviour. That fits the definition of "agenda" pretty well.

So if any "any communication that is calculated to further an agenda" is forbidden, how would you fight the pandemic?

I don't think this is correct. In my experience, most online "fact checkers" seem to get it right the great majority of the time.

Can you point to some examples you are thinking of?

https://www.politifact.com/li-meng-yan-fact-check/

Note they didn't say with scientific humility "we do not know if that scenario actually happened, more data is needed, it's too early to make the conclusion". They say "it's ridiculous and debunked" and rate it "pants on fire" (i.e. an obvious outrageous lie). They act as if they are the ultimate authority with absolute knowledge of the facts and expertise to make such calls - while they don't have neither the facts nor the expertise. And this happens again and again.

You are misrepresenting that article.

Do you believe covid is a bioweapon?

The conspiracy theories these people were pushing as a lab release had themes of gerontocide, eugenics, mind control by 5G, microchipping, general anti-vaxx beliefs most blaming Bill Gates as a sort of Bond villain.

All of these are still being pushed.

Do we have more plausible sources an accident happened? Yes. Was it reasonable to blame China for biowarfare against the whole world including itself, or to accuse Bill Gates for planning to exterminate half the population? No.

Fully agree that Snopes comes off very much in her support here - however, at least they still seem to do their job and describe her actual actions in due detail in the article - even if this leads to a completely ridiculous outcome ("Can bombing a government building really be called terrorism? Hmm, difficult to say...")

This seems better than the OP's fact checker, which just presents the story as "fully debunked" without actually doing so.

Zuck ofc really likes to feed on things. Getting rid of information is okay as long as it doesn't gets in the way of his feeding. FB fact checking is both expensive and crap but still light years ahead of amazon reviews.

I don’t know about you but I don’t like being gas lighted.

I do not believe fact checks. They have zero credibility.