This is a different situation than my.mp3.com. In that case the website stored one copy of each piece of music, required the user to verify they owned it, then allowed you access to their stored copy. This was found to be actionable as they were allowing multiple people to download one master copy of a MP3, essentially repeatedly pirating that MP3.
Amazon is establishing a separate cloud drive for each user. If you buy a MP3 they copy it to your personal drive for you. They also allow you to upload your music to that drive. There is a separate copy of each song stored on the cloud drive for each user, and the only MP3s Amazon copies to the drive are legally purchased. As the user can only download what they have uploaded or purchased, no piracy occurs, at least on Amazon's part. Users may be storing pirated music on their personal cloud drives, but these are private file storage areas and do not allow MP3s to be exchanged among users, thus the cloud drive does not facilitate piracy.