Earlier quoted context omitted.
An NFT is essentially a trading card for the thing that it's attached to. Just like you don't "own" Babe Ruth in any meaningful sense by owning a Babe Ruth trading card, you don't "own" the artwork associated with an NFT by owning the NFT itself. The exception is if there's some arrangement external to the NFT that links ownership of the NFT to ownership of the thing.
Could I sell an NFT for my birth certificate to raise some cash, while my original birth certificate remains at the state's Vital Records Department under ownership of the state? If so, what exactly would the buyer be buying? Just a virtual trading card and a promise that I won't sell my "birth-certificate NFT" trading card to anyone else?
Yes, and it's basically equivalent to writing the words "My Birth Certificate" on a piece of paper and selling that piece of paper. It holds no weight whatsoever.
> If so, what exactly would the buyer be buying?
Nothing.
> Just a promise that I won't sell my "birth-certificate NFT" to anyone else?
Not even that, unless you also did that. You can make multiple NFTs from the same thing. Just like nothing would prevent you from writing "My Birth Certificate" on a second piece of paper and selling that too, unless there was some external agreement that you wouldn't.