Agreed. At the meeting, Barzini sits at the head of the table. After Vito gives his explanation of why drugs will be the ruination of the Mafia, Barzini replies on behalf of the others. When Vito appears to make a concession, Barzini jumps right in: "Then it is agreed--the traffic in drugs will be allowed and Don Corleone will give it protection in the East..." And modern Barzini is the only Don smoking a cigarette--the Moustache Petes are puffing DiNobili's.

The scene in the garden with Vito and Michael occurred after the scene in which Tessio complains that Barzini is moving in on his territories. So it's no surprise that Vito would conclude that Barzini will be the one to make the move on Michael.

The only mystery is: Why didn't Vito know earlier that "it was Barzini all along"? As he told Tom, "Tattaglia is a pimp...alone he could never have outfought Santino." Tattaglia had always been a pimp--didn't Vito know that before the meeting? And, shouldn't Vito have known that Barzini was the number-two Don, and that he'd have the most to gain from the drugs deal, and from eliminating Vito?