Yes, LLMs don't think on their own, for one; they think when you invoke them.
My rebuttal is that people only think when invoked just the same and can enter states where there is no consciousness just the same. The OP has already accepted that LLMs think, but it seems that you are arguing they do not? This car business is confusing and the LLMs not checking themselves is also wrong, there’s even a benchmark for this https://correctbench.github.io/
OP says: LLMs never think when not invoked.
What you said: I have example where, sometimes, human think when invoked.
That's the difference: human brains are intrinsically different because they are built to be able to think without being invoked, even if there are situations where they think when invoked.
There are tons of obvious examples of human thinking without being invoked. Just take a bath and you will see :)