It depends how the question is framed: are you asking to confirm humanity, or confirm LLM.

If you are asking, is this LLM text Human generated, and it says Human (yes), then it is false positive.

If you are asking is this LLM generated text LLM generated, and is says and it says Human (no), then it is a false negative.

That seems like a restrictive binary. Are there not other entities which generate text? What if a gorilla uses ASL that is transcribed? ELIZA could generate text, after a fashion, as a precursor to LLM. It seems like there's a number of automated processes that could take data and generate text, sort of, like weather reports, no?

So I think the only thing a mythical detector could determine would be LLM, or non-LLM, and let us take it from there. But detectors are bunk; I've had first-hand experience with that.