Are sources being double checked, did they attempt to contact the subject of the story for comments, do they have a process for reviewing bad stories and issuing retractions? That's really the difference between The NY Times and some random Macedonian blogger.
It's possible with all of that that the times can be wrong and somebody blogging from their moms basement can have the story right, but in the long run, you're better off getting your news from an organization that follows journalistic best practices.
There is a philosophical discipline devoted to establishing Truth: epistemology. "Criteria of Truth" describe how people can, and do, make judgements on the truth of propositions, in the face of information which is incomplete, confusing, and out-of-date. Correspondence, coherence, and pragmatic theories are the strongest, though other fallbacks, including authority, tradition or custom, and majority opinion are used, despite the fact that they are unreliable.
The ultimate keeper of truth isn't quite the right question, but in general, those who are trusted with distinguishing truths are those who have shown the capacity, ability, and integrity to serve in that role. That is: who judges truth? Someone who is very good at doing just that.
Authorities aren't absolute, they're not perfect, and they're not immune to bias or corruption. But, over time, they should show themselves to be sincere in their efforts to uncover the truth, inclusive of admitting their errors and changing their judgements in the face of new evidence.
The problem is a complex one, but not a greenfield.
It's the same with SCOTUS rulings. They give a detailed account of their reasoning. Even conservative justices who I think routinely use backwards reasoning to make idiotic decisions at least tend to follow a logic absent in rulings from their conservative peers in lower courts (who tend more toward non-reasoning like "gay is bad" and "why do you hate capitalism").
I can at least follow a bizarre logic and understand how they came to the decision because there is a logic, even if the logic comes from a mindset that conflicts with my own.
Getting the answer to the question right isn't particularly useful if the question itself is wrong.