Earlier quoted context omitted.
You can't fool an inanimate object. An LLM is (effectively) just a really, really elaborate "choose your own adventure" book. It's not "working through" problems, it's just tracing a route through an pre-defined information space. It's not actually thinking, it just does a good impression of it.
Please explain why the mechanism of the LLM generating output precludes it from being able to be fooled without using use tautologies or reducing to substrate for explanation.
'Fooling', essentially to deceive or trick, is defined as causing someone to believe an untruth - at least in British English it does.
LLMs don't hold beliefs (neither do mechanistic processes), and they aren't a someone.
You can widen out the definition words but that generally makes language weaker - interestingly, semantic drift is a big issue for LLM's.