They can change the content, you’ll just know they did it. Much like if my watch gets stolen I’ll know, but I still don’t have a watch anymore.

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.

I see no reason they couldn’t change the content rather than just delete it. In fact the article shows an example of exactly that in practice.

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.

The article was about the NFT containing a name. This thread is about "NFT points to a content hash", to quote toomuchtodo. You can't change the content and keep the same hash.

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.