I think people misunderstand when they see that it's a "statistical model". That just means that out of a range of possible answers, it picks in a humanlike way. If the logical answer is the humanlike thing to say then it will be more likely to sample it.

In the same way a human might produce a range of answers to the same question, so humans are also drawing from a theoretical statistical distribution when you talk to them.

It's just a mathematical way to describe an agent, whether it's an LLM or human.