The Cold War was a team effort, but the Pope was instrumental in communicating much of the revolutionary ideas against Soviet bloc regimes under the guise of religious business. Poland, Czchekosolvakia, Hungary, the Baltic states, and even much of the former Yugoslavia are free today in part because of Catholic interference within the Soviet empire. I would imagine that the Pope cooperated with Eastern Orthodox churches in this effort within Russia, as well.
Perhaps you need an extended history lesson about the fall of the Soviet empire from within. I suggest you do some of your own research.
When you were a child, if daddy had allowed you to hit the tree he was felling with your little toy hammer, you might tell yourself that you had a part in the process but that wouldn't make it so. The same holds true with the Vatican's intrusion into world politics, while it's a nuisance and entirely ineffectual, no one wants to be the one to hurt the child's feelings.