That sounds like Anthrophics watermark explanation though.
Wouldn't that mean that checking the watermark...
(1) Required knowing the prompt used to generate the text; and
(2) was just as expensive as generating the text?
(One approach that's been described is creating a bias in certain token pairs or short sequences: by hashing the previous n tokens, potentially with a secret seed, you create a list of essentially random allowed and disallowed next tokens, then bias the token selection to prefer allowed tokens, so long as they are plausible enough. Then you can check any long-enough subset of the output, if it deviates significantly enough from random chance on following this rule, it was almost certainly generated from a system following these rules.)