No, you own the NFT, which people value because the artist issued it.

Cool, if you want to pay real dollars for a digitally signed link to a web resource, go ahead.

The link is a red herring. Just like an original Picasso, the content of the thing you own is responsible for very little of its value (an excellent forgery would deliver all the aesthetic value of the original, but it would be much less valuable). The provenance of the thing is the reason it is valued. There’s really nothing new or unique about NFTs other than the technology used to implement them.