The LCA principles also make the careful and critical distinction between input to train an LLM, and output—which could potentially be infringing if it is substantially similar to an original expressive work.

from your second link. I don't often see this brought up in discussions. The problem of models trained on copyrighted info is definitely different than what you do with that model/output from it. If you're making money from infringing, the fair use arguments are historically less successful. I have less of an issue with the general training of a model vs. commercial infringing use.