I personally think aggressive fact checking authorities impedes this process, because people don't change their minds when faced with authoritarian power against which they are powerless, and because they are powerless here, they get angry and they disengage. This ends up which reinforcing their beliefs and now you've lost all chance of change.
One such instantiation of this: https://chomsky.info/consent01/
Now, consider that in most "free speech" societies, those with money can repeat things many orders of magnitude more than others. Over time, this results in influence. Thus, while many countries have "free speech," I'd say they don't have "fair speech." The two concepts complement each other, but one is not the opposite of the other.
If these "facts" are so obviously facts, we wouldn't need a team of researchers to establish the fact whether they are facts.
The fact that these "facts" need to be "fact-checked" means they are so open to interpretation and depend on context, that we came to the conclusion that this "fact-checking" concept in fact does not really work.
You can still "fact-check" for yourself; do your own research, make up your own mind yourself. Then you will become more of an independent thinker, be less influenced by authoritarian figures.