Brand new facts generally go through a public disclosure process where some established institution (a news outlet, academic journal, whatever) is willing to vouch for it as true, or at least vouch for it as being worthy of consideration and discussion— and in any case, will strive to present it with the appropriate context and framing as far as level of certainty, who the players are and what their motivations are, etc etc.

I think it's reasonably fair for the policy for nobodies posting on social media to be that "new facts" (or "original research" in Wikipedia parlance), particularly those which may be harmful to public safety or marginalized groups should be either unpostable, or considerably reduced in how far they're able to spread organically (shadow-banning).

If you don't like it, go to some other social media network. For my part, I'd be content with a Facebook feed where none of the posts I'm seeing are "new" facts. OTOH, I'd also be content with a FB feed that was exclusively pics of my friends and their kids and very little news or politics at all.

In this case I assume the BMJ article was peer reviewed, so it was already fact-checked by knowledgeable individuals. BMJ is a reputable journal that can be relied to fact-check their articles. The fact that it was labeled a newsblog means that the fact-checkers really had no domain knowledge about the facts they were supposed to check.

Science has come up with peer review for that purpose. It is far from perfect but works more often than it does not.

Outside science I would recommend to delegate fact checking to knowledgeable persons. For brand new facts ask an expert.

Expertise isn't a cure all. An example is the famous Minux/Linux fight. Tanenbaum was a distinguished professor, arguing with some guy on the internet who built a kernel. "Is a monokernel a viable way to build a first rate operating system?" Fact Check: operating system researchers widely believe that monolithic kernels are a fundamentally flawed way to build a system...

The premise that there are some specially endowed people who, by virtue of their credentials, are the only ones able to mark things as true sounds like the core tenants of a religion, not a secular society!