They wouldn't own the art. They'd own the tweet of the art, but not the art itself. You also don't have to worry about copyright, or legal, contracted ownership and rights of use. NTF minting and sale doesn't impact that at all. It's just a unique number attached to a specific digital file.
Beyond that, all of this is way too new to have any kind of meaningful legislation behind it. I'm ambivalent on the whole thing; I think NFT's could be cool once the environmental issues are addressed. (A major positive change in that regard is slated to be implemented sometime in 2022.) But until then, I'm avoiding it. (Those ridiculous GAS fees help squelch any temptation.)
I've blocked the accounts doing tweet minting, and I'd suggest everyone else does so too until there's more clarity as to what 'owning' a minted tweet, or art piece, or whatever, actually means.