There is a huge lack of insight into who owns the copyright of an NFT. This confusion likely stems from the fact that an NFT comprises two things: (i) the identifiable, non-fungible, non-replicable, and transferrable cryptographic asset recorded on the blockchain, and (ii) the creative content. The creative content is separate and distinct from the actual asset recorded on the blockchain. As such, the person or entity that created the creative content owns the copyright. The content creator continues to own the copyright, even if the NFT is sold to someone else. It’s analogous to Jeff Koons selling artwork he created—Koons can sell the art to one person to hang on their wall, but since Jeff also owns the copyright, he can sell that same artwork as an image on t-shirts.
No, the "non-fungibility" simply means that anyone who creates an NFT with the same link will be distinct from your link to the image, even if the actual URL is the same. Both NFTs can also be traced back to when they were created/minted because they're on a blockchain, a property called provenance. If the authentic tokens came from a well known minting, you can establish that your token is "authentic" and the copy token is a recreation, even if the actual link (or other content) is completely identical.
Nothing about having the "authentic" token would give you actual legal rights though.
For a contract transferring property, you need 2 parties: One offering and the other accepting. Having knowledge of a cryptographic key implies none of that.
You could get something like this done by transferring the asset to a reputable trustee. The trustee - a law firm, bank, or such - checks that the paperwork is in order and it has the necessary rights. It binds itself contractually to convey some benefit - eg a revocable copyright license - to whoever can show that they have a certain cryptographic key/control of a wallet.
The firm should regularly check if the beneficiary still holds the key. It might get lost or forgotten, after all. The possibility of losing access to the asset by theft or accident is the only thing that involving NFTs add to such a scheme, so one might as well lean into it.
Be a shame if I traded my stupid collection of URLs around and eventually bought them back only to lose the key, better get insurance in case I forget it.
At best you're buying into a collective agreement of ownership among those also participating in the NFT ecosystem. You own a thing because a large enough group of people agree you own it and respect the authority of that token.
At worst you've been scammed and are trying to convince yourself the above is true and that said "large enough group" includes anyone at all capable of enforcing said ownership. Spoilers: it does not.
You click it. You see the image in your browser, assuming the server it links to is still running and the owner of the server has not deleted the image.
Then you right click and save the image. Like literally anyone else can do.
NFTs are great for replacing things like deeds or vehicle titles, where we need paperwork to verify ownership. But the problem arises when it's cryptographically hard (meaning exceedingly unlikely on reasonable timescales) to reverse fraudulent transfers of those documents. Cutting out a centralized authority at the price of making the system more vulnerable for gullible people is almost always not worth it.