What you always assumed to be true, is according to the Italian government

Pope's Shooting Laid to Soviets by Italian Panel: New York Times

Citing new photographic analysis, an Italian parliamentary commission has concluded that top Soviet leaders were behind the failed plot to kill Pope John Paul II in 1981...

The new claim revolves largely around two new analyses of photographs of the crowds in St. Peter's Square that day. The analyses show decisively, the report says, that a Bulgarian, Sergei Ivanov Antonov, the former director of Balkan Air, was in the square at the time of the shooting and so had lied when he said that he was in his office at the time.

Mr. Antonov and two other Bulgarians were cleared by an Italian court in 1986 of accusations that they had hired the Turkish gunman, Mehmet Ali Agca, who was convicted of attempted murder and was imprisoned in Italy until 2000.

Agca might be insane with his legion of stories, each one different, about how he came to shoot the Pope.

I've always thought the Italians were wrong to release him without a verifiable confession from Agca identifying and implicating the people who paid him, gave him phony id, weapons, etc.