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?
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.