Proposition: Equal records can hide a surviving-state difference

There are complete one-outcome instruments with identical record laws and residual trace distance $1/2$ on one qubit input.

Proof. Compare the identity residual channel with computational dephasing, each carrying the same single classical symbol. On $|+⟩⟨+|$, their outputs have residuals

Their difference has eigenvalues $1/2,-1/2$, so its trace distance is $1/2$.