yeah, this is the rather basic flaw in what lots of people, including on HN, are proposing:
They seem to demand a sort of proof from first principle for journalism, where every reader can (and must!) verify an article without any heuristics such as a medium's track record ("Argument from Authority!", they will complain, "FALLACY!").
Yet such a system is simply impossible. In practice, because nobody would ever have the time & energy to verify any meaningful fraction of the information they consume. But even in theory, there just aren't any methods to distribute "proof": you could be an eyewitness, which doesn't scale. You could inspect original documents, which also doesn't scale, and where almost nobody has the expertise to actually verify them. Oh, and then there are distributed ledgers, which could help around the margins but nobody knows how (Bitcoin, incidentally, is the outgrow of exactly the same mechanism, only for the financial system: the breakdown of trust in institutions such as the law or the FED, and the attempt to replace it with technology).
One of many incarnations of this dynamic the widespread criticism of the use of anonymous sources. And while the practice does have its problems, it's almost universally misunderstood by those criticising it today.
When journalists use anonymous sources, they substitute their own reputation, and that of their publication, for the source's. Which is why, when you go back and read articles from a year or so ago, you'll find that each and every single anonymously reported fact has actually been proven correct, or remains unknown. The system works (worked), because everyone in it is playing the long game.
But that would require trust. And people today aren't just distrustful. They completely deny the utility of the concept. They try to evaluate all information with complete disregard for the source (and fail). They assume equivalence between anonymous internet commentators and institutions such as universities, newspapers, or established politicians, without even noticing how this conflicts with their criticism of anonymity as described above.
This mindset is related to a perversion of the scientific method, one that denies the usefulness of all emotion, of the social sciences, and of all human relationships. It's perverse because even its proponents entirely fail to live by it: if you're more willing to let your spouse borrow you car than just any stranger, you're using the very same mechanisms (familiarity, the game theory of long-term relationships, reputation) that you otherwise reject.
So that's a long-winded way to say: these fact-checkers are supposedly different than whoever posted the material in question. You, and everyone else, can observe them over time, and they will have a reputation to defend. They will presumably also be recruited from the set of people and institutions that are established as trustworthy, at least among the minority that still believes in such a thing might actually exist.