Flagged "human" but actually "LLM" is not a false positive, but a false negative.
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.
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.