But the bank's reputation for skulduggery goes back further, almost to its inception in 1942. According to American intelligence documents cited by the author Ferruccio Pinotti, a group of leading Italian industrialists met in Turin in 1945 to discuss how to conduct the forthcoming war against communism in Italy.
One of their first moves was to deposit a large sum in the Vatican, presumably in the newly-founded Vatican Bank.
Licio Gelli, the former head of the outlawed P2 masonic lodge, which counted ministers, secret service chiefs and other representatives of the Italian elite among its members, now effectively acknowledges that both the Vatican and the CIA were allies in his organisation's struggle against Marxism.
For example, Cardinal Alfredo Ottaviani, chief doctrinal watchdog at the Holy Office until the mid-1960s, was a friend with whom Gelli dined frequently, despite official Catholic disapproval of freemasonry.
"One might say Cardinal Ottaviani was our spiritual father, because he was from the very far right," Gelli told me in a recent interview.
"He had a sister who was even more fascist than Mussolini," Gelli laughed, remaining an unrepentant fascist himself.
He also admits to knowing successive CIA station chiefs in Rome, sometimes taking new arrivals on an introductory tour of the country.
Gelli also said that Marcinkus had participated in the war on communism. "Above all he was there to make money," the former masonic leader said.
Marcinkus, an American of Lithuanian origin, used to handle security on foreign trips for Pope John Paul, collecting financial contributions from Catholic industrialists in the countries the Pope visited.
It was Calvi, Gelli said, whose Banco Ambrosiano had been squeezed to finance anti-communist operations, including subsidising the Polish trade union, Solidarity.