No, that would actually be feasible with enough effort.

The real question is what do you do if someone takes a screenshot of that image? Since the picture must be in a format that can be shown, nothing is stopping people from writing software that just strips the authentication from the camera file.

Edit: misread the problem. You need to get a private key to make forgeries and be able to say "no look, this was taken with a camera". Stripping the signature from photographs is the opposite of what we want here.