Aside from the editorial control over which facts are included/omitted, that you rightly mention, the bigger issue with facts is who gets to decide which facts have been proven, and which haven't been. If you accept the premise that there are no universal truths, no facts that have been absolutely proven and can never possibly be falsified (a premise that you're free to reject, though I'm rather certain no proof of fact exists that cannot be invalided by the munchausen trilemma), then you should also accept that the process of validating a fact is naturally subjective.
The role of the fact validator is to evaluate the proof, and decide whether it meets a subjective criteria that elevates it to the level of fact. Controlling this process allows the fact validator to decide which information is fact, and which is not. Even when you have a rigid criteria for evaluating facts, the criteria itself is going to be subjective and opinionated, and no matter how much you try to control it, the fact validator will have some leeway in interpreting the criteria and how it applies differently for different facts.
This is one of the roles of a jury. When a jury is presented with conflicting accounts of facts (as they often are), one of their jobs is to review the evidence and come to a consensus on which facts (in their opinion) are true.
There's also the issue that statements of fact, and statements of opinion are not quite that clear cut. Consider the statement "He attempted to undermine the process", which is the sort of thing I could hypothetically imagine a fact checker attempting to validate. It's a statement of opinion that potentially alludes to statements of fact. If you break it down into how you might reach that conclusion, you'd have: "He did a thing" this is a statement of fact (whether it's "proven" or not). "The thing he did undermined the process" this is more of a statement of opinion, as it presupposes what the process is intended to do, and how the thing he did influenced that. "It was his intention for this thing that he did to undermine the process" and this is unambiguously an opinion as all cases of attributing a motive are naturally opinionated.
But keep in mind that this whole argument I'm making is based upon the idea that there are no universal truths (which relates to philosophical ideas like relativism and absurdism). These ideas have their critics (such as Plato who criticised Socrates' interpretation of them), but I've never heard any satisfactory (according to me) explanation of how you might go about proving a universal truth (with universalist ideas typically only being embraced by religion, and perhaps ironically the anti-religion moral universalist camp, people like Richard Dawkins)