The Jesuits aren’t secret guys. They teach at universities and are out there in public. They also have a wide spectrum of points of view. If you wanted them to get organized like the KGB, it would be like herding very smart and stubborn cats.
I am fairly sure that the guys at Georgetown are not exactly thrilled. Francis can greet them and say, “I have understood you. He will not stand them up against a wall, but he is not their friend.