Allen Dulles and John Foster Dulles certainly didn't play nice. The list of things that they messed up, and too big to hide from being on the record, is quite illuminating (Vietname, Cuba, China/Taiwan/Tibet, Korea, Indonesia, Iran, Iraq, Egypt, most of south america really, and so on) which suggests far more things occurred in the shadows too. A couple of Italians is small peanuts in comparison, especially since by 1960 the possibility of Italy flipping to the Soviets was gone. The secret agreement to base nukes on Italian airbases would have been signed around this timeframe, so Rome wouldn't have protested, really quite clever.

Also the organizational and logistical possibility was very real too considering that enormous sums of money were diverted off the books for funding secret projects in that period. In fact, even up to early 1945 nobody in Congress knew about the real purpose of the manhattan project (which was consuming a sizeable chunk of the national budget!). Not even Harry Truman, who was Chairman of the Senate Subcommittee on War Mobilization at the time (who was given the run around by Stimson).

Though to be fair it was not just Washington, all the powers invested in covert, off-the-record, stuff to some degree. French/Israeli/Indian/Pakistani/South African/etc. nuclear bomb development being the most well known examples as again they are too big to fully cover up.