Corollary: If you can't use the output to train, then you don't own them.
There might be a few exceptions, if you really guided your model in a certain particular way, but that is rare.
What /could/ be is that you violate their ToS. If that ToS is valid and legally and practically enforceable is a different question and will depend a lot on your jurisdiction.
It’s kind of like causing what Google Docs autocomplete sentences helps someone write is still.. theirs.
It's named "yours" at the time of payment, but actually only a license to use under certain conditions.
This basically makes their AI useless.
Originally it was not that way. They changed it because, as you suggested, their service has questionable utility without it.
The outstanding one is the “meaningful human input” part of copyright. The most recent ruling is that prompting alone does not count. If you write/rewrite sections, those are yours. Everything in between is a somewhat untested.