Why it does not contradict plateau covariance

The vector field defining the witness is supported in the ramp, not in $U$. It specifies an allowed background $w=K\xi$. The no-go tests the response on all backgrounds; it does not apply a forbidden parameter as a plateau symmetry.

Conversely, X-F's direct identity uses parameters supported in $U$, where ${\sigma }_{\epsilon }=1$. These are distinct tests.