iphone 5 Camera broken on arrival.

So I received my iphone 5 today, pluggled it in to itunes and everything went fine. Then a little later I tried to use the camera, and the phone got stuck on the shutter opening animation. I tried other camera apps and they just showed a black screen.There was no physical damage to the shipping box or the phone. Everything else on the phone worked fine, just the camera. After troubleshooting with the help of Apple care for an hour, still broken. I was told to go to Verizon where I ordered the phone from. After walking 3 miles to the Verizon store, they told me it would be faster to just have Apple send me a replacement. After talking to multiple Apple support employees they said they can express ship me a new phone, but charge me $30 for shipping. I refuse to pay them to replace my DOA iphone. Is it wrong of me to feel that the charge should be waved and that I should be compensated in some way?