Does anyone understand exactly how Paulie sold out Vito to Barzini by simply calling in sick? I know it's very minor, but it's always kind of bothered me the way it is presented. It doesn't make any sense to me. If Barzini and Sollozo needed help from someone inside the Corleone Family, don't you think they would have had that person actually do something rather than just call in sick? I would think it would make more sense to actually have the betrayer there. If Paulie hadn't called in sick that day, he would have been the only one there with Vito, so why have him call in sick? By Paulie calling in sick, they knew Vito would have had to get another bodyguard, one who could have possibly thwarted the asassination attempt. If anything, Paulie calling in sick would seem to make their attempted hit more difficult.

Godfather experts, am I missing something that would make Barzini's plan seem more sensible, or is this just one of those instances where it's a movie so not everything has to make sense?