The truth is the truth---cheap oil made the USSR unable to buy Eastern European manufacturing goods causing the Eastern Block to break apart. The vatican had no role in the break up other than a superficial one in Poland.
"What has happened in Eastern Europe in recent years would not have been possible without the presence of this Pope, without the great role even political that he has played on the world scene" - Mikhail Gorbachev quoted in La Stampa, March 3, 1992
This is an excerpt from the PBS's leftist Frontline - it is the conclusion of a piece that (lest you think it overstates his role) very thoroughly points out that some people make false claims about what Pope John Paul II:
http://www.pbs.org/wgbh/pages/frontline/shows/pope/communism/
From the first day of his election, John Paul II's pontificate raised concern in Central Committee headquarters. The Canadian reporter, Eric Margolis, described it this way: "I was the first Western journalist inside the KGB headquarters in 1990. The generals told me that the Vatican and the Pope above all was regarded as their number one, most dangerous enemy in the world." Soon enough, people of all sorts--world leaders, clandestine dissidents and ordinary Catholics--sensed the Communists were impotent before the Polish Pope. In 1979, when John Paul II's plane landed at Okecie Airport, church bells ran throughout the country. He criss-crossed his beloved Poland, deluged by adoring crowds. He preached thirty-two sermons in nine days. Bogdan Szajkowski said it was, "A psychological earthquake, an opportunity for mass political catharsis..." The Poles who turned out by the millions looked around and saw they were not alone. They were a powerful multitude. The Pope spoke of human dignity, the right to religious freedom and a revolution of the spirit--not insurrection. The people listened. As George Wiegel observed, "It was a lesson in dignity, a national plebiscite, Poland's second baptism."
Our images of revolution are filled with blood-stained pictures: French aristocrats lined up against the Bastille wall; the Tsar's family executed in a cellar under cover of night; Mao's victims floating down the Yellow River. The romantic collective Polish psyche brims with images of violent, quixotic rebellions. They range from the futile uprisings of the 19th century to the calvary charging German tanks on horseback at the beginning of World War II. But the revolution launched by John Paul's return to Poland is one that conjures roads lined with weeping pilgrims, meadows of peaceful souls singing hymns, and most of all, of people swaying forward as one--reaching for the extraordinary man in white as he is borne through their midst. "What is the greatest, most unexpected event of the 20th century?" James Carroll asked in his interview with us. "Isn't it that the Soviet Empire was brought down non-violently? Isn't John Paul II's story part of it?"
Again and again, people told us that it was. John Paul II's 1979 trip was the fulcrum of revolution which led to the collapse of Communism. Timothy Garton Ash put it this way, "Without the Pope, no Solidarity. Without Solidarity, no Gorbachev. Without Gorbachev, no fall of Communism." (In fact, Gorbachev himself gave the Kremlin's long-term enemy this due, "It would have been impossible without the Pope.") It was not just the Pope's hagiographers who told us that his first pilgrimage was the turning point. Skeptics who felt Wojtyla was never a part of the resistance said everything changed as John Paul II brought his message across country to the Poles. And revolutionaries, jealous of their own, also look to the trip as the beginning of the end of Soviet rule.
It took time; it took the Pope's support from Rome--some of it financial; it took several more trips in 1983 and 1987. But the flame was lit. It would smolder and flicker before it burned from one end of Poland to the other. Millions of people spread the revolution, but it began with the Pope's trip home in 1979. As General Jaruzelski said, "That was the detonator."