And if you look closely at that scene, Barzini gives himself away. He, not Vito, sits at the head of the table. He, not Vito, takes the lead in the discussions--and he jumps the gun on Vito by declaring: "Then it is settled. The traffic in drugs is allowed, and Don Corleone will give it protection in the East. And there will be the peace." (He's also the only Don smoking a cigarette--the others are smoking cigars.) I think Vito deliberately let him show his hand.
The only thing that surprises me is why it took Vito so long to figure out that it was Barzini all along. "Tattaglia is a pimp; alone he could never have outfought Santino." Well, Tattaglia was a pimp all along--why didn't Vito see that Barzini, younger than the other Dons and more ambitious, would have the most to gain?
Well, Vito had almost died, and he was out of the loop. The last real business he did was with Solozzo, and at the time they thought it was quite an accomplishment to have "discovered" that the Tattaglias were bankrolling him.
If you recall, the last thing Vito did was to have Luca Brasi go sniffiing around the Tattaglias to find out what was under Sol's fingernails. Had Vito not been shot, he would have realized it was Barzini sooner...keep in mind the next time Vito did any business was after Sonny died, and within the time of one meeting he realized it was Barzini all along.
