I agree with Lilo. In the fishtank scene, Vito asks, "Do you trust my judgment?" "Always, Godfather," says Clem, with feeling. "Yess-ss," hisses Tess. If I remember correctly, Tess exits hastily, without a handshake. I think he sent out feelers to Barzini soon afterward. I don't think Barz attempted to turn him first, much less at Vito's burial.