For a given short-context (hash function seeding) you do have detectable manipulation of the completion (how they can read the marking). But, because (assuming enough entropy in context) the hashing function is decoupled from the log-probs, the perturbations are independent from the underlying distribution, so you're still sampling from the same distribution quotient some noise.

The only way you'd notice this is they weren't independent, and the most plausible way that happens is if you're re-completing pre-fills (resampling the same hash function against the same log-probs).