Not disagreeing with you. Just saying that this is the exact purpose of the NFT - to show that you are the owner of the digital piece, i.e having the receipt/bragging right of it. It has nothing to do with the distribution. Anyone can have a copy.
Claim of ownership is overrated.
It's just a record on a blockchain.
It is trivial to fork said blockchain, and have a conflicting claim setup on the fork.
It’s harder to fork the Ethereum blockchain in the same sense that it’s hard to convince people to accept factorial bucks over old fashioned USD.