No, you dont need the UPC, or the box...I'm not sure if you need the receipt though....I didnt, when I RMA'd my 6800GT. Call them....dont worry about the BFG, they are American, and they speak ENGLISH! (no overseas outsourcing crap).
They just wanted me to use a traceable carrier (FedEx, UPS, etc), put it in a anti-static bag, and use shock absorbing packing material, such as peanuts/bubblewrap.