Let me give you a specific counterexample: it's easy and common to generate phishing emails. Trust in email has not dropped to the degree that phishing is not a problem.
Phishing emails mostly work because they apparently come from a trusted source, though. The key is that they fake the source, not that people will just trust random written words just because they are written, as they do with videos.
A better analogy would be Nigerian prince emails, but only a tiny minority of people believe those... or at least that's what I want to think!
That's the point. They do, but they no longer should. Our technical capabilities for lying have begun to overwhelm the old heuristics, and the sooner people realise the better.