Do you not crypto? It's clear which address mints an NFT, and that address can be provably linked to the party with the keys. And they can put that proof on their website. You do know your favorite artists website, right?

So yeah, by looking at both NFTs we can clearly determine which is authentic.

If they're supposed to be unique, as opposed to 'we both sponsored the same art', then there are easy ways to ensure that.