Hagen had to be at the Sol meeting because he set it up. Logically, Vito wouldn't have included Sonny if, as the novel strongly implies, Vito's mind was already made up to say "no." But, since Vito had included Sonny in the pre-meeting discussion, he had to be at the meeting. And, more important, Puzo needed to present us with Sonny's indescretion to set up the shooting, Sol's post-shooting proposal to Hagen, and Michael's descent into murder.