That is the issue, you just rephrased it to sound softer (public knowledge isn't a legal term). Fair use law isn't supposed to apply to commercial activity. So it is absolutely about using copyrighted work for LLM training.
No, otherwise there would be a straightforward "non-commercial" clause. Instead there's a 4 part test, which takes usage (commercial or not) into account, but doesn't hinge solely on it.
>... In determining whether the use made of a work in any particular case is a fair use the factors to be considered shall include:
>1. the purpose and character of the use, including whether such use is of a commercial nature or is for nonprofit educational purposes;
>...
If they really meant "non-commercial use only", they sure did spend a lot of words to not say that.