Sorry, but your local instructor is mistaken. It's unfortunate, NY has no reciprocity with any other state. They just plain stink. Even upper NYS and Long Island license holders can't bring their guns into NYC, but NYC residents with their licenses are recognized in the rest of the state.
Someone should have the guts to take away the right of NYC residents from stepping one foot outside the city with their weapons. I think things may very well change, but it hasn't been attempted. Police Officers and retired police officers, which I am fortunately one of may carry everywhere.
It really stinks how superior this state regards itself.