I think the lagambi not inducting the men merlino wanted proves the opposite. Why woul merlino want ligambi to induct merlino's own guys into ligambi's crew???? If merlino told him to induct them it proves at least merlino, mazzone and ligambi is in the same crew, ligambi just didn't feel comfortable with the guys merlino wanted inducted

"McGurn likes you, so I make you. So you are now one of us, if you fuck up, we take it out on McGurn. He is your sponsor. Fuck up, it's his ass. You work in his crew, he is your capo."