Others have pointed out that this is a clear way in which cloud storage is fundamentally different from local storage, which one might not expect -- being able to be secure in one's papers, a fundamental right in the US, only pertains if the papers are physically located on your person or property.
I'm overextending here, but I think the physical analogy applies as well -- if the police want to search a rented storage locker, the search warrant is served to the storage company, not the lessee of the locker.