Everyone is applauding this because they hate Trump, but take a step back and see the bigger picture. This could backfire in serious ways, and it plays to Trump's base's narrative that the mainstream media and tech giants are colluding to silence conservatives (and maybe there could even be some truth to that.) I know the Valley is an echo chamber, so obviously no one is going to ever realize this.
Completely agree with your second point though (not that there is any collusion to silence conservatives - but that this whole situation will be taken that way and used to energize that base).
What is the most annoying about this, though, is the tweet they chose to "Fact Check". (I use quotation marks because "fact checking" by linking to CNN and WaPo is not fact-checking at all, rather an appeal to a different authority.)
The tweet they chose to police is speculation about the future. If I say the boiling point of water is 50 degrees, you can fact-check that. Its an objective truth that water boils at 100c.
If I say mail-in votes will cause election fraud, you cannot prove or disprove that statement. All you can do is show me someone else's statements, opinions, and predictions on the matter.
Given that Trump says so much objectively false stuff, it annoys me they didn't go after one of those tweets instead.
You catch the most flak when you're over the target...