What I'm particularly interested in here is stuff that proposes to use NFTs as avatars or something similar - if I go mint my own counterfeit ape and make it my

What I'm particularly interested in here is stuff that proposes to use NFTs as avatars or something similar - if I go mint my own counterfeit ape and make it my avatar, are those apps going to happily display that I have "verified ownership" of it? Is there any recourse there aside from every app locking down to an explicitly allowed list of keys from "verified NFT producers," or every app playing whack-a-mole with the keys of known bad actors, or establishing some sort of off-chain database of content hashes and the keys that are supposed to own them?