You should absolutely be able to get a working iPhone. Either yours will be repaired or replaced. The Genius Bar person should have advised you how to proceed - I'm not sure whether that would be returning the iPhone to your service provider and getting a replacement from them, or having the Apple Store handle it (though I would think if that were available, the Genius certainly would have advised you).
For future reference, as I am currently using my tenth iPhone, I purchased exactly one from my carrier (because in 2008 that was the only way to receive a corporate discount with that carrier). I purchased the other nine from Apple, so there would be no question who would handle issues in the event of problems (I never had any).