That's untrue. See my comment elsewhere around here. It doesn't rely on the commercial aspect, though if it's not commercial the bar for fair use is set lower.

The argument in Warhol relies on the fact that the derivative work, ie, Warhol's painting, is substantially similar in function to the original photograph. If Warhol had used the picture as stuffing for a soft sculpture, it would not infringe.

LLM is closer to the latter than the former.