In the long run, I wonder if all video will be signed via blockchain-or-other-trusted-3rd-party. You'd need everything from the camera to the the editing software to support it though.
Otherwise you can just feed whatever video you have in mind into the first stage of that chain you’ve created and say you were there when it happened.
You could then use that internal state as a private key to sign what you want and only keep the corresponding public key and a signed date+time to proof the veracity. The public keys themselves would need to form a blockchain in the traditional sense, so you can verify their integrity without the previous internal states.
If you wanted to go all-in with the verification, you'd probably also want to show something containing the date+time in the video, together with some complicated physical effects that are hard to fake.
Well, just thinking out loud here, but it seems like it might work :D
It seems like this trivially works better with a centralized database especially since you don't necessarily want to make all of this data public. The general public needs to know that this is a true and accurate photo that hasn't been edited taken on such and such a date. The authorities with a warrant might well need to know that it was taken by a device owned by bob.
We can't inherently trust content on the basis of its medium.