The original BMJ article doesn't draw any conclusions that I can see. It certainly doesn't suggest the Pfizer vaccine is unsafe or ineffective, as the "fact check" heavily implies.

This one is a more in-depth rebuttal to the article and indeed BMJ itself; I found it compelling. https://sciencebasedmedicine.org/what-the-heck-happened-to-t... It argues that the article was disingenuous to the point of being propaganda.

It almost certainly does. They even block out a box of their conclusions in grey to draw the reader eyes.

Additionally, the fact they never reached out to the companies at all is telling enough of their agenda.

People on Facebook aren't actually reading the journal. They're looking at the title and saying "see, the vaccine was unsafe all along." The fact checkers said "Missing context ... Independent fact-checkers say this information could mislead people" which is absolutely true.