I think they mean it like this: imagine you ask me a random number sequence. I give you a random number sequence. Little did you know, I used a very specific PRNG to generate it, so later I can prove with certainty that your number was generated by me, and you can't say you came up with it yourself.

There is no room for false positive here in the same way you can't randomly find a collision in a hash function if it's strong enough. Like the rate is so infinitesimal that it is effectively zero.

Now replace random number sequence with prompted string of words. And instead of using the PRNG on every word I use it every n words. If the generated text is sufficiently long I can tell by matching the expected deterministic pattern.

You can defeat it by changing the words yourself and triggering a false negative but there isn't really any room for a false positive if the text is long enough and the pattern matches perfectly. If the pattern doesn't match then I can compute a probability.