Yeah this isn't really true. There's not how humans work. For a variety of reasons, Plenty stick with their incorrect model despite the world indicating otherwise. In fact, this seems to be normal enough human behaviour. Everyone does it, for something or the other. You are no exception.
And yes LLMs can in fact tell truth from fiction.
GPT-4 logits calibration pre RLHF - https://imgur.com/a/3gYel9r
Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence Scores from Language Models Fine-Tuned with Human Feedback - https://arxiv.org/abs/2305.14975
Teaching Models to Express Their Uncertainty in Words - https://arxiv.org/abs/2205.14334
Language Models (Mostly) Know What They Know - https://arxiv.org/abs/2207.05221
The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets - https://arxiv.org/abs/2310.06824
Your argument seems to boil down to "they can't perform experiments" but that isn't true either.