Fortunately, it's pretty simple in real life. We have certain publications and sources we trust, whether they're the NYT or a respected industry blog. We know they take accurate reporting seriously, fire journalists who are caught fabricating things, etc.
If we see a clip on YouTube from the BBC, we can trust it's almost certainly legit. If it's some crazy claim from a rando and you care whether it's real, it's easy to look it up to see if anyone credible has confirmed it.
So no, no worry at all about the past being erased.