Indeed it was plaw's type of question. That wonderful guy and I (and many others here) went round and round on the old issue of five vs. six families.
But I doubt that the Bocchicchios were the sixth family, if there was a sixth family. If memory serves, the Bocchicchios were limited by a "strain of stupidity" that ran through them. They were "straight from the shoulder people who knew how to bribe a policeman but didn't know how to make overtures to politicians," or some such. Dominating the garbage business in an upstate NY community is a real Mafia activity. But augmenting their income by hiring out hostages is not the stuff of a major Mafia force. How much face would they lose if part of their business was to have their members killed by other Mafia families?
Let me offer a real-life parallel:
Francesco Uale, aka Frankie Yale, was a reputed big-time Brooklyn racketeer who was Al Capone's mentor, and who sent the young Capone to Chicago to Johnny Torrio. But Capone and Torrio later hired Yale to whack Dion O'Banion for them. A real big-time racketeer doesn't hire himself out to do hits.