Was it really Barzini all along?

I am convinced it was. He was a deep player who attacked from any sources, including trusted friends.

During the funeral, Tessio conveys a proposal for a meeting with Barzini, which identifies him as the traitor that Vito was expecting. Michael arranges for a series of murders to occur while he is standing as godfather for Connie and Carlo's son. Pete Clemenza shoots Don Stracci and his bodyguards as they exit an elevator. Moe Greene, while having a massage in one of his hotels, is shot in the eye by an unknown assassin (this form of execution was later known as the "Moe Greene Special"). Don Cuneo, while leaving a hotel, is trapped in a revolving door by Willi Cicci and shot twice. Don Tattaglia and a prostitute he is with are gunned down by Rocco Lampone and another unknown assassin. Finally, Don Barzini is shot on the steps of a courthouse by Al Neri, who is disguised by wearing his old policeman's uniform. Michael's presence at the baptism gives him a perfect alibi. After the baptism, Tessio believes he and Michael are on their way to meet with Barzini. Instead, he is taken away by Willi Cicci and other buttonmen to be killed. Before he is carried away, Tessio tells Tom Hagen that he always liked Michael and his betrayal was simply just business.