The extra rules really only apply when for one reason or the other we've assumed that some exterior system which doesn't obey QM interacts with a QM system obey

The extra rules really only apply when for one reason or the other we've assumed that some exterior system which doesn't obey QM interacts with a QM system obeying the schrodinger equation. The exact border between when this is a valid assumption and we can apply extra rules to make up for it vs. an invalid assumption is ill-defined.