LLMs have absolutely nothing to do with truth. If anything the analogy is closer to syntax as LLMs are pure form, just language in absence of any context or reference.
LLMs tell you one thing and not its negation, this choice is semantic. "just language in absence of any context or reference" is a set that includes every valid text. The usefulness of LLMs is their ability to mostly respect whatever semantics you establish in the prompt in their choice of output.