If we're being serious about cryptography, you could have cameras signing videos in real time with a secret key, in such a way that each camera has an individual key stored in a specialized chip that does the signing, with no way to access the key without breaking the chip's seal.

So you could still fake videos, but any accusation of tampering could be verified by checking the seal is intact. (of course you need non-forgeable seals too, but that's comparatively easier)

Generate random key every hour, sign it with previous private key, then delete previous private key.

If (honestly I've no idea) we can produce cameras that have a higher FPS than the display's refresh rate (or resolution), then we'd be able to detect that.

A simpler detection mechanism would be to use stereoscopic (or rather real depth detection) cameras though.

No need to think that far. Just calculate the hash of the video file stored on camera (or segments of it during e.g. live stream) and authenticate this using a private key stored in a secure element on the camera. Do you trust this secure element enough (see the breach of Intel’s CPU Private Keys via SpecEx, maybe you can do so by loading a custom firmware as well?).

Assume the secure element is in fact secure, the issue then, as with any public/private key scheme, lies with establishing trust of the keypair. Do you trust the manufacturer that he will not be breached?

And more pressing even; How do you prevent someone modifying their internal camera video stream such that they may send any data to the authentication chip/mechanism?

And if all this is implemented, it can be done even more low level - just direct the camera e.g. to your screen (I assume solutions would then crop up to increase the fidelity of such a solution).

I am not saying such a solution would not provide ANY benefits, I am just pointing out that these issues prevent it from becoming a silver bullet.