I saw this article https://medium.com/initc3org/copyright-vulnerabilities-in-nfts-317e02d8ae26 that someone mention before about how NFTs related to copyright and it brought up an interesting point, what couples the NFT to the physical artwork, if I have the art but someone else has the NFT who's the real owner.
I think it depends on what's your idea of ownership and how the owner decided to assign ownership of the particular IP/art. If the owner says that the IP is owned by whoever owns the NFT, then that should be the de-facto standard IMO. Of course, when selling the IP, other people may think differently and see possession of the physical item as true ownership - this affects the value. I do think that if an artist meant to couple the NFT and physical item, it's more of a thorny topic but if I'm not wrong usually it's commonly viewed that you need both to have true ownership. So in your case, it might be accurate to say that neither of you have true ownership over the art piece.