For discussion. Speculative. Feel free to criticize.
Let us consider the possibility that Pope Francis accepted the nomination to be Pope with good will, to help stabilize the Church in a time of crisis caused by Benedict the XVI stepping down. Let us say that a small group of Cardinals were responsible for the nomination and perhaps counseled him to take it. Let us say that Francis may have been a little naive about what he was getting into, and put a lot of trust in a small group of people (perhaps this group perhaps another). Let us consider that this group guided him on what to do, how to act, etc., and he went along with it.
Let us say that when he read the Vigano letter he realized that these counselors were using him to do the very opposite of what he thought he was doing (stabilizing the Church). Where does that leave him? He is asked a question on the plane and cannot answer it (yet).
What would/should he do? I suspect he may resign, Benedict XVI may step in temporarily and call another conclave.