They can delete the content. That's the only "change" they can do. It's like your watch analogy, except you can easily back up an image, but cannot back up a watch.
Sure you can back up an image, but the backup is worth the same as a copy of the NFT: zip. You now own a pointer on the blockchain to nothing and a jpeg on your disk. I’ve got a lot of that going on already with zero expenditure.
Similarly, you can prove to others that the version on your disk the version pointed to by the blockchain by having people check the hash.