I think it's unlikely for a viewer of Part II to think of Barzini at that moment. Especially one of his remnants trying to avenge Fabrizio's death. We have hardly any indication Fabrizio was real close within the Barzini Family? He was on their payroll while bodyguarding Mike in Sicily, and therefore they arranged his emigration. He worked in a pizza place now, right? Why should he be an active member of the Family? And if he was, he was not a high ranked one, so who would want to avenge? Also, there's no other indication in the entire movie someone from the other NY families is interest in the 'death of Michael Corleone'... in fact it always bugs me a bit that we hardly see anything of the Five Families and the Commission in part 2 & 3...very little at least... in real life, those NY families were 'all that' in the mafia. they seem to be unimportant in the two sequels. therefore I don't think you would link Fabrizio's death to the Tahoe shooting