I'm going to snip the quote tree, but it's much the same when you live in parts of New York state that aren't, well, New York City.
In fact, I just visited NYC for the first time a few months ago after a lifetime spent in New York state!
A few of mine who grew up in the same hometown (very rural part of the state) went to college out of state and constantly had to deal with people who assumed she was from NYC. When they learned her hometown had more cows than people and one stoplight in the entire municipality, they were dumbfounded.
One person actually tried to argue with her that she couldn't have grown up in New York, it must have been Pennsylvania or Ohio or something.
Trying to explain that I live in a city in New York state that isn't New York City can get brain-hurty as well.