You’re missing the point. OK, it’s not ‘thinking’ in a pure sense; the point is it’s private notes. If someone says something to you, they are allowed to privately prepare it first (thinking, jotted notes, LLM rewriting, running it past lawyers, whatever) and you don’t get to see all that. That’s how it has always been.
Just because someone says/writes something to you doesn’t mean you have any moral right to see all the things they considered and then decided not to say.
Firstly, this is just wrong. People can and do search stuff online as they're writing something up.
Second, your distinction is the one that's meaningless. The LLM could be running locally on a private machine...