I do not have to trust my teachers on what the answer is to a math problem: I can check it. Likewise for history - I can refer back to the sources they are quoting from. One lesson we've learned in the West is that often times our understanding of an event evolves - much of what I learned in history class we consider to be incorrect today.
Education is not telling someone what is true or not true, it is to train the methods of discovering truth and disproving lies. It is critical thought.
A fact check, and more egregiously censorship directly is against critical thought. It tells us that most humans are not fit for handling complicated problems or balancing sources - that instead we must trust some other authority to do that. It does not require a long search through the history book to find egregious mistakes by every journalistic outlet running today - including those purporting to be fact checkers.
If humans are unfit to engage critically with diverse information than so are the fact checkers. There is no human who is so trained and intelligent as to be unerring in their judgements and fact findings.
History doesn't repeat, but it has it's tropes. The well-intentioned erosion of freedom of speech and the subsequent censorship is not new. It will get worse before it gets better.
