We've had to confront similar issues with other media earlier in history, after all.
Let's not just establish a new proxy for implicit trust here.
The fact that you can't imagine – and I don't provide – any alternative proposition does not make implicitly trusting video a good proposition.
But, yeah, I suspect reality will probably disappoint us both...
We'll need to deal with video the same way we do with images, audio, and eye witness accounts. The way to do that is to establish a measure of trust in some quantifiable or methodological way, rather than just trusting the medium.
People don't like it when nobodies are filming them, even in very public spaces. For some reason they are ok with CCTV, despite that not being much different (I do recognize that cctv is typically recording a general area and isn't always HQ)