If you plug your UPS tracking number into packagemapping.com, you get a bit more information, including two additional reference numbers (on top of your phone number and order number). One looks like it may be another phone number, perhaps an Apple number, but I have no idea what the forth one is. I thought it may have been a serial number but I plugged it into Apple's site and didn't get a hit.
You don't need another website to get all the various tracking reference numbers. On the UPS My Choice site, once you bring up your package (in Detailed View), off to the right side, you'll see up to six reference numbers (including your Apple Order ID and your phone number).On the UPS website? How do you see reference numbers on the UPS site?
