I do not have the time to work through every part of the example, but imo the main claim is still overstated. Showing that a result would be extremely unlikely under a particular null model is not the same as showing that it is “statistically impossible” for a human to produce. It also does not give a guarantee how the text was written. A tiny p-value is still a probability under assumptions and not a proof of provenance.

Furthermore, a human does not even need to know the secret key. By pure chance a human written text can display an unusually high alignment with the detector’s secret partitioning.

The published watermark work, which is also cited by the article, appears to be much more careful about this (based on a quick skim). It reports false positive/negative rates, thresholds, length requirements, and more. Those can be very strong results, provided the assumed conditions apply. They do not turn a detector into an infallible test. Moreover longer text only helps if the assumptions and watermark signal actually remain intact, which can fail in general.

In such controlled settings, sure, I do not have much issues there. But the claims of “a human cannot replicate this” or “we can guarantee the text was generated with the watermark” are much stronger than the statistics, and especially the cited literature, actually appear to support.