Whilst Carlo is not in the muscle-end of the family....

Smug Carlo could have run to Barzini gloating that the Corleones have no idea it was Carlo who helped Barzini, set up Sonny's murder
The Corleones are fleeing to Nevada and Carlo's gonna be Michael's right-hand man The inside man, for Barzini

Barzini might, he just might....buy Carlo-Tessio-Barzini deal / Barzini-Michael meeting

The only Don material Sicilian member of the family Don Carlo!