It's like you said, "...our much older and simpler systems... keep us grounded in reality."
Memory is far from infallible but human brains do contain knowledge and are capable of introspection. There can be false confidence, sure, but there can also be uncertainty, and that's vital. LLMs just predict the next token. There's not even the concept of knowledge beyond the prompt, just probabilities that happen to fall mostly the right way most of the time.
We don't know that the mechanism used to predict the next token would not be described by the model as "introspection" if the model was "embodied" (otherwise given persistent context and memory) like a human. We don't really know that LLMs operate any differently than essentially an ego-less human brain... and any claims that they work differently than the human brain would need to be supported with an explanation of how the human brain does work, which we don't understand enough to say "it's definitely not like an LLM".
Memory is far from infallible but human brains do contain knowledge and are capable of introspection. There can be false confidence, sure, but there can also be uncertainty, and that's vital. LLMs just predict the next token. There's not even the concept of knowledge beyond the prompt, just probabilities that happen to fall mostly the right way most of the time.