You can, but it will then be obvious to anyone familiar with the references or who has the power of reasoning that you have failed (innocently or not) to consider them, not that you have found something that debunks them.
The point of declaring true/false is to have the final word for most readers. "No need to look further, Snopes said it's true". Sure, anyone can provide evidence to say you're wrong, but they're just some random blogger and nobody reads them. And on the off-chance that someone big picks them up, you apologize, adjust the verdict, and move on.
You don't need total control over the information of 100% of the population. Having a lot of control over the information diet of 70% of the population is great already.
Yes, it does.
> Anyone familiar with the topic will already know what’s up, and anyone interested enough to research the topic will be able to do so as well.
They will be able to do so…by reviewing and evaluating information from sources that provide the evidence and logic on which they rest conclusions. That a “fact checker” is such a source is…clearly something that matters.
> The point of declaring true/false is to have the final word for most readers.
And the point of providing support is to provide the ability for the readers that are willing to do more legwork to evaluate the claims, which is also how a fact checker gets (or loses, either because it fails to do this or because following back doesn’t support their claims) the reputation which allows them to be trusted by the users that don’t do the extra legwork. Same as any other source, because all a fact checker is is another research source that happens to be focussed on claims of current salience and controversy.
> “No need to look further, Snopes said it’s true”.
Which only holds up as a long as Snopes reputation holds up.
> Sure, anyone can provide evidence to say you’re wrong, but they’re just some random blogger and nobody reads them.
That would be a problem in a world where Snopes was the sole and universally accepted “fact checker” and every other source of information was regarded as “just a random blogger”. But there are lots of fact checkers (both standalone and as part of media organizations), and a lot of focus by interested parties with very influential platforms on the reliability of various entities that hold themselves out as fact checkers or other fact sources.
The whole point of "fact checkers" is to be used by people who are not expert on the subject
A fact checker is a (usually tertiary, like an encyclopedia, providing references to primary and secondary sources) source that is distinguished by focussing on current, controversial claims. There is nothing more a "fact checker" can be. That's not a failing, that's an inherent limitation given the nature of facts.