Do you honestly believe Ecuador will initiate hostilities against NATO in order to protect a foreign citizen from due legal process in that persons home country?
It would surely be less effort and risk to lift him from the roof by helicopter and whisk him to a waiting jet James Bond style.
They probably would not call it an act of war without backing it up --so I doubt they would. If they did bluff and get called, next time hostilities flared up with Peru or Columbia, they might not be taken seriously.
