I'm reading Joe Bonanno's book at the moment. We all know he's lied about certain things, but I don't see any reason why he would lie about this.

He says there was an alliance between Genovese, Luchese and Gambino against Costello and Anastasia. Profaci and Bonanno were kind of in their own conservative faction. He also says it is likely Gambino used his own men to to kill Anastasia.