Re: They're already doing this
Maybe have video recording devices use a private key to encode their identity into the recording, so if you could present the phone that made the recording into evidence it could be proven that the video shown is as was originally recorded by the device and not modified?
That'll work until someone manages to set / recover the secret key, or finds out the algorithm* that sets them.
I estimate about 3 days after it gets to market, after a 6 month pre-launch advertising / promotional drive saying how such a thing it can't be done.
* "But we seeded rand using time() and the serial number and then encrypted it with base32 AND uuencode, and then rot13'd the result nine hundred thousand times, just like it says in the stack overflow comments! No one can break that!"