This story is literally about a single instance. By that logic, a single instance where fact checkers proved something was false is enough to justify their existence.
As the BMJ article points out, Cochrane has had the same problem, and it's not like these are the only two cases. There have been huge numbers of statements by high profile experts and professors being labelled as fake news by journalism interns at "fact checkers". You may not be aware of them but this is a very frequent problem.
No, not by that logic. The logic is "some people claimed that claims of the possibilities of bad outcomes were instances of the slippery slope fallacy, and now that the bad outcomes were actually realized, they should apologize, because something isn't the slippery slope fallacy if things further down the slope have actually happened". That's not even remotely connected to anything you said here.