A330
the NAV ADR DISAGREE (or the NAV AOA DISAGREE depending on the model) caution is necessary when one of the three ADR was already declared faulty or it was switched OFF and there is a disagreement between the two remaining ADRs (or AOAs, depending on the model).
This caution does not protect us from a treacherous failure of two ADRs or AOAs in such a way that their error is coincident and it has the effect of declaring faulty the only healthy ADR. It is a necessary caution, since with only two ADRs there is no possible voting.
What protects us is that, every time an ADR is declared faulty we have to be healthily paranoid and check that it is OK that ADR #x has been correctly rejected (or not). All the more if the reason of the rejection is a disagreement of one versus the other two. That is why I would appreciate to get that information.
Now I think that the best way to give this info could be a extra line below the NAV ADR FAULT caution (something like DUE ADR DISAGREE?) when the reason of rejecting is the result of a voting.