Actually, in NYC one cannot even possess one's own shotguns and rifles. Have you ever heard Rush talk about the hunting rifles he was offered while he lived in the city? He refused the gift because of the legal hassles involved with owning them (and securing secure off-premises storage) within the boundaries of NYC.
In Binghamton, where I live, your statement is correct.
That shows you how long I've been out of NY. Back 10 years ago, my friend got an SKS while living in NYC, and did not mention any license being needed -- he just bought it and took it home.