Your comment in particular made me feel like it was worth posting!
We mustn't confuse attestation with reputation, nor even the combination of attestation and reputation with truth.
Attestation is nothing more than someone staking their reputation on the veracity of what they're sharing with the world.
If I'm being frank, I thought this was too obvious to need stressing. If the camera is pointed at David Copperfield, cryptography can't make the lens show you reality.
Attestation solves a lot of problems, but like my first sentence said, video integrity isn't a problem which can be solved anymore, if it ever was.
I’ve written a blog post that addresses many of problems, and your comment was one of the reasons I posted it! You can find it at https://news.ycombinator.com/item?id=33558566
What we can have is attestation and reputation, then provenance.
It starts with a container format that allows signatures of both the entire video with audio, audio only, and video only, along with reasonable segments (three seconds?) of each of these.
Excerpts of any of these can be transcluded into another such container. The editor can transform it in any way, the resulting display doesn't have to match the particulars of the excerpt (captioning, noise filtering, color correction) but the excerpt is itself included, or at least the signature.
It would be useful for some people to have cameras which do this at the moment of recording, along with GPS, cell location data, and so on, to get really bulletproof documentary footage.
I don't want that built into my phone, necessarily. As a container format and ffmpeg style tool, this would support anonymous attestation which can be demonstrated by the keyholder at any future time. As a built-in subpoena-able feature of my phone or mirrorless camera? Hmm, probably don't want that. If it snitches proactively, not a chance in hell.