Let a person lose a right to truth whenever the truth would foreseeably and materially contribute to his doing an evil. And so the (sigh) Nazis at the door (groan) lose their truth rights for the same reason that an insane man loses his gun rights.
But why is it shameful to lie one’s way out of martyrdom? It’s worse than this: in lying your way out of martyrdom the one you are lying to by definition lacks a truth right, so your public profession of faith would be a case of giving someone something they have no right to. So now we’re committed to a morality that turns martyrdom into a sort of theft or despoiling of goods. We’ve probably made a wrong turn somewhere.
So maybe we add an epicycle and describe truth rights as being lost whenever truth would foreseeably and materially contribute to doing an evil to someone other than yourself. Even of we get past the stink of the ad-hocery, this still leaves us with something of a Monty Python martyr trial: three believers get tried together and, while each person confesses they are guilty the other two loudly protest “No he isn’t! We’ve never seen him before!” After all, we can’t just say that the others should keep quiet: that would be the moral equivalent of doing nothing when the suicidal man had a gun.
So the flip side of right-to-truth claims is that they involve a limitation on professing fidelity. Religious faith would be a paradigm case, and other sorts of fidelity would be limited a fortiori. Right to truth claims seem to have some difficulties accounting for our need not just to know truth but to be faithful to it.