SIGHASH_ANYPREVOUTPUT Question: Won't the eltoo proposal allow someone to transfer ownership of bitcoin at an address without a chain transaction?

SIGHASH_ANYPREVOUTPUT

Question: Won't the eltoo proposal allow someone to transfer ownership of bitcoin at an address without a chain transaction?

If it's possible to fashion a new signature that satisfies a transaction requirement even after an eltoo transaction is in the UTXO, and also makes previous signatures obsolete (nSequence), won't it be possible to create a signature that authorizes a subsequent signature and transfer ownership? Thus transferring ownership of a UTXO without anyone being aware?

Am I mad for thinking this? Or just dumb?