Rizzitiello at some point asked NY for create a separate family,but NY said no. Anyway having no italian presence,the L.A. family survived accepting to made mobsters that shouldnt be made in other families.
The "second family" narrative was something pushed by Craig Fiato, who is not reliable in this regard. Rizzitello had his issues with the Milano faction but it's clear there was only one family in Los Angeles as evidenced by his associates being made or otherwise proposed for membership into it (Comparetti, Nick P. Nardi, Paduano, Fiato to some degree)
As for the rest, it varied per member. Jimmy and Charles Caci as well as Stephen Cino were carried by the FBI as Buffalo members at several points - Jimmy as late as 1983
They were all well respected within the national network whereas on the other hand you had guys like Michael Esposito, who was assaulted on several occasions as a Lucchese associate and then someone like Russell Masetta, who probably would never have been an LCN member if he didn't marry into the Milanos
