I'd go for unanswering*. Maybe unanswerable, but to me that's less clear.
*I'm not sure there is a single word in English that would fully encompass the meaning as I understand it in the given sentence.
I did look up unimpeachable, and found this info. on impeach interesting:
Word History: Nothing hobbles a President so much as impeachment, and there is an etymological as well as a procedural reason for this. The word impeach can be traced back through Anglo-Norman empecher to Late Latin impedicre, "to catch, entangle," from Latin pedica, "fetter for the ankle, snare." Thus we find that Middle English empechen, the ancestor of our word, means such things as "to cause to get stuck fast," "hinder or impede," "interfere with," and "criticize unfavorably." A legal sense of empechen is first recorded in 1384. This sense, which had previously developed in Old French, was "to accuse, bring charges against." http://www.thefreedictionary.com/impeachHey--the French word for going fishing is
pêcher
, and look: Anglo-Norman empecher ..., "to catch, entangle,"
