assuming there are two fact-checkers who have a contrasting conclusion, both get reliable sources, who are we going to trust?
for example, this article about covid vax deaths i have linked before also contains numerous sources on their claims. no matter how misrepresented to you, under your logic, this too should be considered a fact-check.
They won't listen to you. Often, the Covid data I link to is from ourworldindata, which has a huge number of independent sources from all around the world. But they don't accept this, because... well, because they don't want to. I've yet to see a valid reason for their objection to it.
the biggest problem isn't about fact-checking, but there are authorities censoring any counter-fact-checking practices, which is already happening, such as YouTube banning vaccine misinformation. in fact, this kind of practice isn't telling those information wrong but what information they fear people talking about.