What is and isn't fact is for people to decide by themselves based on evidence. Not whatever Twitter decides is the truth. There are very few hard facts in this world especially surrounding politics.
Surely this is false. The world is full of hard facts—politics less than the sciences, sure, but still [0]. What are much rarer (non-existent?) are undisputed facts.
[0] To be clear, I distinguish hard facts in politics, like "Trump is the 45th president of the United States", from hard facts in political science, of which there indeed seem to be very few.
That is why Twitter is linking some facts to go along with the President's tweets.
You need a really good reason to take away Twitter's editorial control over Twitter. Please provide one. (The best I see so far is "Twitter is really popular, so they shouldn't be allowed to edit their own website." I am not convinced that that is a good justification for limiting the freedom of the press. If that's where we want to go, I would be the first in line to make sure Fox News drops their conservative bias and gives liberal viewpoints a fair shake. Does that sound good to you?)
For almost 100 years it has been held both in general and by the Supreme Court in particular that the remedy to speech you disagree with is more speech. Do you object to Twitter's ability to have such a disagreement?
Or, as is being proposed, do you believe Twitter should be held legally liable for every nasty thing said on their platform simply because they choose to have an opinion of their own?
To me that seems like a recipe for significantly more banning of content & users by Twitter to avoid even the hint of liability that would come with allowing it to stand.