So sometime between the multiplayer Beta and the Blackout Beta this week Activision removed the ability to redownload the Beta in preparation for Blackout. Two days ago I found a loophole that allowed me to download it again after I deleted the Beta to make space. That loophole no longer works today, and Activision aren't letting players download it till it's already live.
This is on top of the Beta only running for 3 days on Xbox/PC versus the 7 on PS4. PlayStation also had the ability the preload. Based on the fact that they removed the ability to download it and then even fixed a loophole that allowed users to download it really makes this sound like part of the exclusivity deal involved not allowing Xbox to even preload it. The Beta is almost 20GB and some users won't even be able to download it before the end of the Beta.