It appears that Modern Warfare 3 DLC downloaded by CoD Elite subscribers can only be played by the profile that downloads it.
Usually, content downloaded to an Xbox console, including games and DLC, can be played by any profile on that console.
This doesn't sit well with users who note that the download's Terms and Conditions clearly state:"You can use this item on the first Xbox 360 console you downloaded it to. Access to this item will also be granted to all users on this first console."
An official response on the matter is yet to be issued.