Facts are verifiable data.
Some people call things facts that are not facts.
How people present facts may be false or incomplete, but facts aren't, they are still verifiable data.
It's possible to be deceptive and still use facts, after all, you can mix them with lies, but it still doesn't change that facts are facts. If you do fact checking, you are verifying the data of the statement. If it passes, it's actually a fact and not a fake. If it fails to be verified, odds are you are looking at a lie.
What's so bloody hard to understand about that?
Oh yeah, people have been suckered in by 'truthy'. That old set of lies that is present as facts that you don't want to try and verify because you want to believe them. Sorry, but fact checking shoots those lies down too.
Perhaps you're worried that the fact checkers won't actually check the facts and lie about it. That is a possibility, but there are always more fact checkers out there to check over the other fact checkers. Anyone who does the research to verify data is a fact checker, even if you're an amateur. Fact check the fact checkers, and if you find they've screwed up or lied, let everyone know, and you can bet the scandal that would cause will get their butts back in line and checking properly again. Either that or wipe them out entirely.