You're as native to New York as the horses that came over on the Mayflower. As a native American, its always a trip to see immigrants looking down on shiner, newer immigrants. Talking about natives and non natives like that means anything in a gateway city like NYC, SF, or LA is laughable.
You can be a South Brooklyn chump all you want. It doesnt mean youre any more "new york" than an Amish kid who came up to the city on rumspringa and never left.