That's not actually correct, JB. (I do love your upstate-bashing, though!) Originally Marble Hill was attached to Manhattan, but a canal was dug in the Harlem River which separated it from Manhattan and put it on the mainland. Though it has always been part of New York County, it is generally regarded as the Bronx. It looks like the Bronx, it feels like the Bronx, the address says Bronx, NY 10463, and the area code is 718.
When you're walking down Broadway, Kingsbridge (Bronx) becomes Marble Hill (Manhattan) after W 230th St, but there is no "Welcome to Manhattan" sign.