Fact checking shouldn't be controversial
General comment here, not just to one specific poster. What the BBC and the Guardian et al are conveniently forgetting to mention, and it drives me nuts, is that what has been 'fact checking' on platforms like Facebook has been censorship.
Try saying on FB, probably even still today, one's perfectly legal belief in the UK or US that 'biological sex is immutable and that this matters in life and law'. Then wait for the ban-hammer to fall as it is classed as 'hate'. The rise of this kind of censorious activism, of which H&M are proponents, was a very important part of why Harris lost the presidential election, and it needs facing up to not batting away as an inconvenient truth.
Interestingly, Facebook / Meta will still have moderation, but they are moving the operations out of California, the heartland of censorious activism, and into Texas, a state that has been attracting a number of content creators these past six months who feel battered by the chilling effect of censorship elsewhere.