So I finally got a response from EA, here it is:
Thanks for updating me on this issue regarding the freezing you've been experiencing with NCAA Football 07 on your Xbox 360 game console. Seeing how the game is consistently freezing on your console, it would be my belief that the firmware for your DVD drive in your console may be at fault. Unfortunately, this is not something that our engineering or development teams can affect as this appears to be a hardware issue.
In further researching both the Xbox and the Xbox 360, I have found that there are differences in the component hardware used in the consoles' construction and these subtle differences oftentimes result in instances where game freezes may occur. Again, when this happens, generally a firmware update will correct this issue but, in the case of the Xbox and Xbox 360, this will have to come from MS as they control all aspects of their hardware. Our development team, while very sympathetic to your plight, has done everything necessary to fulfill the specifications of the Xbox 360 based on the information provided to us by MS. What you may want to check are which other options you may have with regards to updating your firmware through MS and the Xbox customer service team. If, because of this shortcoming, you are completely dissatisfied with NCAA Football 07, there is very little other option I can provide aside from offering our 90-day warranty so that you exchange the game with a brand new, sealed copy for return to your original retailer.
There's some more, but it just tells me how to return it to them.
So basically it doesn't work on some 360's because of an incompatibility with their dvd firmware.