This is a baseless assertion of emergent behaviour.

> Every time a bot searches

We are talking about LLMs by themselves, not larger systems using them.

> LLMs ability to separate facts from expression is quite well developed

It is not. Whether you ask an LLM for an excerpt of the bible, or an excerpt of The Lord of the Rings, the LLM does not distinguish. It has no concept of what is, and what is not, under copyright.