Video evidence is relatively easy to fix, you just need camera ICs to cryptographically sign their outputs. If the image/video is tampered with (or even re-encoded) the signature won’t match. As the private key is (hopefully!) stored securely in the hardware IC taking the photo/video, any generated images or videos can’t be signed by such a private key.
getting the picture to perfectly replicate the image on the screen without it being noticeable would be so difficult it would probably be easier to modify the camera instead