That’s not how copyright law works.
Commissioned work is owned by the commissioner unless otherwise agreed upon by contract.
So long as the work is not distributed, exhibited, performed, etc, as in the example of keeping the artwork on their refrigerator in their home, then no infringement has taken place.
> [If commissioning some work and] keeping the artwork on their refrigerator in their home, then no infringement has taken place.
I'd like to push back on this: Is that legally true, or is it infringement which just happens to be so minor and under-the-radar that nobody gets in trouble?
Suppose there's a printer in my room churning out hundreds of pages of words matching that of someone's copyrighted new book, without permission.
That sure seems like infringement is happening, regardless of whether my next step is to: (A) sell it, (B) sell many of it, (C) give it away, (D) place it into my personal library of other home-printed books, or (E) hand it to someone else who paid me in advance to produce it for them under contract.
If (A) is infringement, why wouldn't (E) also be?
Ownership of artwork is independent of copyright infringement. Derivative works qualify for their own independent copyright, you just can’t sell them until after the original copyright expires.
Just because I own my car doesn’t mean I can break the speed limit, these are orthogonal concepts legally.
> Commissioned work is owned by the commissioner unless otherwise agreed upon by contract.
I think the LLM example is closer to the LLM and its creator being like a vendor selling pictures of Indiana Jones on the street corner than hiring someone and performing work for hire. Yes, if it was a human artist commissioned to create an art piece, then yeah, the commissioner owns it.