Earlier quoted context omitted.
The watermark would still be there. You can take a photograph of the image with an old Polaroid and, if the resolution is high enough, the watermark would still be there.
If it can be detected, it can be removed. Asking that false things carry claims of falseness is a dead end.
Let's now let's say your AI deepfake image is watermarked/hashed upon generation. Difficulty: Intermediate to hard. You might be able to get it done, but not without real effort, and removing all traces of the watermark without leaving artefacts might be so difficult as to be nearly impossible.
...So it doesn't eliminate the possibility of fakes, but it hugely raises the cost and effort bar. Only the most motivated would bother.