The dual channel version of this would be where both parties understand each other's language, but use translators anyway for diplomatic nicety, so they can get

The dual channel version of this would be where both parties understand each other's language, but use translators anyway for diplomatic nicety, so they can get to brass tacks* with each other but the historians record the encounter in a highly refined register. * Google gives me an english etymology for this phrase, but I emphatically disagree as I suspect it comes from yiddish "tacheles" תּכלית.