Well now Microsoft changed the terms around:
If you're an original Xbox owner with a paid Xbox Live account and purchase an Xbox 360 between November 21 and December 21 of this year, you'll be entitled to a free copy of Bungie's sci-fi opus. As it's not present inside the console's packaging, you'll have to wait for Microsoft to mail the game to you (it arrives by January 18, 2008). After unpacking your new system, you'll be expected to convert your Xbox Live account to a Gold subscription, and enter your details, including the system's serial number, into this registration page before December 21.