Carlo wasn't inside the family business and had no upfront reason to have contact with Barzini. Michael crapped him up about being his "right hand man" in Nevada (where Carlo was born), but they weren't in Nevada yet. Though Barzini recruited him to set up Sonny, Barzini would be giving his trap away if he used Carlo to set up the meeting. Neri and Rocco were loyal to Michael and in any event wouldn't have logical reasons to have contact with Barzini. The "protocol" would be for Barzini to contact one of the caporegimes, or Tom. But in the novel, recall that Michael speculates on who Barzini would contact. "Someone like me," Tom muses. "No, you're too close to me," Michael replies, "and besides, you're Irish." "I'm German-American," Tom replies. "To them that's Irish," Michael answers. He also rules out Neri because "Neri was a cop."