Producing a copy of a copyrighted work through a purely mechanical process is clear violation of copyright. LLMs are absolutely not different from a copier machine in the eyes of the law.
Original works can only be produced by a human being, by definition in copyright law. Any artifact produced by an animal, a mechanical process, a machine, a natural phenomenon etc is either a derived work if it started from an original copyrighted work, or a public domain artifact not covered by copyright law if it didn't.
For example, an image created on a rock struck by lightning is not a copyright covered work. Similarly, an image generated by an diffusion model from a randomly generated sentence is not a copyrightable work. However, if you feed a novel as a prompt to an LLM and ask for a summary, the resulting summary is a derived work of said novel, and it falls under the copyright of the novel's owner - you are not allowed to distribute copies of the summary the LLM generated for you.
Whether the output of an LLM, or the LLM weights themselves, might be considered derived works of the training set of that LLM is a completely different discussion, and one that has not yet been settled in court.