The concept of fact checking is a very recent movement, with the idea that we could filter out the "fake news" on the internet, which is also a recent concept.
But it turned out that the so called "fake news" wans't always so fake, and that the fact checkers weren't always so factual.
So it turns out that you can't trust any group to determine what the facts are for the rest of the people.
You can fact-check for yourself, but don't put your "facts" on other people like they're real facts. Leave other people in their respect, and let them think for themselves. You can of course share your knowledge, but you should let the other person ultimately decide what they believe for themselves.