If the bits that make up the video as was recorded by the camera don't match the hash anymore, then you know it was modified. That doesn't mean it's fake, it just means use skepticism when viewing. On the other hand the ones that have not been modified and still match can be trusted.
Are you saying Apple and Google can't put a secure hash into the output from their camera apps that apply after their internal processing is done?
As far as recording a monitor, I guess, but I feel like you can tell that someone is recording a monitor.
As far as editing, no it wont work in those cases, but the point here is not to verify ALL videos, but to have an easy way for people to verify important videos. People will learn that if you edit it, it won't be verified, so they will be less inclined to edit it if they want to make it clear it's an authentic video. Think like people recording some event going down on the streets etc or recording a video message for family and friends.
If AI video generation is going to get that good, don't you think it would be a good idea to have a way to record provably authentic videos if we need? Like a police interaction or something. There is no real reason to need to edit that.
Also, could a video hash just be computed every X seconds, and give the user the choice to trim the video at each of those intervals?