When you say refund, do you mean money restored to credit card? Or store credit? Mine was a gift, so that might make a difference for me.
I also really like my Band 2. But I have a feeling i'd be just as happy with a Band 1.
Well, here's the deal. When I bought my Band 2 in December, I ordered a size small from Dell.com (some sale + coupon). It was too small, so I took it into the Microsoft store and asked if I could exchange for a medium. They wanted a receipt and I told them I didn't get it from the Microsoft store. After checking with the manager, they allowed the size swap since it was brand new. I did purchase Microsoft Complete (at the time of exchange) for the Medium, so they had my credit card info. This meant I now had a Microsoft store receipt because of the warranty purchase/size swap).
When I went in yesterday with the issue, I asked the guy if the return would work since my receipt was only for an exchange + Microsoft Complete ($39+tax). He said "let's run it and see." Sure enough, $250 went back to my card. So I kinda made money on the transaction, an unexpected surprise. The manager that helped me was all but steering me to just return it. His tone made it sound like they are getting droves of complaints, so I just bailed on the Band 2. Miss it, but don't want another one that will just break as well.
So I don't know how they would handle a true gift with no receipt, but it's worth trying. Worst case I'd imagine is they replace it. If they do, purchase the $39 complete, which will give you a receipt. If it breaks again, return it for a refund that will be processed to the card you used to buy the complete warranty. Worked for me anyhow. I wasn't trying to work the system - they seemed to be encouraging me to just return it, so I took the offer.