Example: Equal quantum marginals, different complete local inputs

Start with a Bell pair at $P,Q$. In one exceptional update, measure the $P$-half in $Z$ or $X$ and deliver its bit $b$ to $Q$. The joint record–qubit states are

Both quantum marginals are $I/2$, but the joint states differ. Measure the qubit in $Z$, obtaining $a$, and report $a\oplus b$. The laws are respectively ${\delta }_0$ and the uniform law. This violates original-metric autonomy, not affinity or equality of laws on equal complete inputs.