True, but not the only relevant thing.
If the output of the LLM is "not very different from the original work" then the output could be the infringement. Putting a hypercomplex black box between the source work and the plagiarised output does not in itself make it "not infringing". The "LLM output as a service" business is then based on selling something based other people's work, that they do not have rights to.
It's falling for misdirection, "pay no attention to the LLM behind the curtain" to think otherwise.