The mistake is in treating the LLM as just another deterministic, narrow computer program it can reason about. It's not. It's a "DWIM" system, and unless you can always precisely express what you mean - which you can't (not the very least because often people only realize what they meant after they get a result that's not it) - you have to treat the LLM as a human-like component. It's what it was designed to be anyway.