Ownership is not the same as authorship. Copyright is about authors rights, not owners.

If you buy a text of me, I cannot sign away my authorship, and there’s certain limitations on what you can do with my text regardless of contract. I can only sell you usage rights - which may or may not be exclusive. If the text I wrote is trivial, neither you nor me can limit when it is reproduced. The effort of collecting data is not sufficient, if the data itself is declared trivial. See rulings about phone books.

When an AI provider produces data that is deemed not copyrightable, it cannot legally sell you exclusive usage rights. It can give it to you exclusively, but since you cannot yourself claim copyright, the moment you publish it it becomes available for others to use as well. One may argue that an LLM is similar to a phone book, with its entries being “trivial“ and its composition not artistic enough.

At least that’s the line of argument.