Absolutely, that is the job of journalists.
But if we face an information apocalypse, it's because many people can't distinguish between good and bad journalism. If the data journalists base their work on was open, I believe we could do better.
> If I read something from a source I don't know anything about, I must keep in mind that what I'm reading just might not be true.
Indeed, that's what you should do, given current constraints. You shouldn't verify by repeating the work the journalist did, because you'd never have time for anything else. But you shouldn't have to repeat it -- it could be available. They already did the work; all they'd need to do is encode it in a readable, searchable way.
Moreover such a system would let us leverage far more peoples' input. While the barriers for entry have fallen sharply, it's still hard to build a readership, because it takes a while to convince people to trust you. If it were easier to evaluate the output of budding bloggers, they wouldn't have to waste a decade shouting into the void before making a difference. (The death of local news is a big problem. This might help, among other problems, that one.)
And, hopefully, through the same mechanism, it would become harder for a propoganda outlet to establish themselves.