Puzo writes

"There was Anthony Stracci, who controlled the New Jersey area and the shipping on the West Side Docks of Manhattan. He ran gambling the in Jersey....etc., etc."

But Stracci is the first of the "representatives of the Five Families of New York" that Puzo describes, and he ends his description with these important words, which serve to further bolster the case for six families in total:

"Of the five New York Families opposing the Corleones his was the least powerful but the most well disposed."

You could also argue that Cuneo was not a New York City family head either, since he is described as the head of "The Family that controlled upper New York State", and no mention at all is made of any activities of his within the city itself.