This is the problem with "fact checking". It positions the platform as an authority. Now, any claim that isn't "debunked" by this "fact checking" gains a certain amount of credibility by comparison. The moral hazards are enormous, multiplied by the opaque behavior of Facebook's algorithm and again multiplied by its unprecedented reach in society.
What about things that Facebook does take down, like fraud and scams or misinformation about voting requirements? Is that problematic because it positions Facebook as an authority about those things? Should Facebook remove posts which claim an election date has been moved, or that if you reply with your bank account details you will get some free money?
It's tempting to say they can take down things like fake election dates without causing any concern, and that's probably true. But there also isn't much that falls in that category, and people can still send such messages via other messaging platforms like WhatsApp, email, the web etc. So it may simply not be worth the slippery slope in the end.