I know this was a rhetorical question, but I'll answer anyway: It isn't possible. Not only is there no way to read latent data normally from a drive that has been zeroed (drives that fail this test are called "defective"), but it is currently understood that recovering data from a modern drive that has been overwritten with a single pass of random data is impossible at any expense.
http://www.cs.auckland.ac.nz/~pgut001/pubs/secure_del.html#E...
However, data can still leak out of cloud stores in the same way that it leaks out of solid-state disks and even magnetic disks: there's no guarantee that a given logical block will always be mapped to the same underlying hardware. A mirrored drive may be fail and thrown in the trash with data still on it, or written blocks might be mapped to different places in an array for any number of reasons. This shouldn't result in leakage to other customers although it is up to the vendor to make sure this doesn't happen.
Depending on the implementation, vendor-supplied encryption may or may not mitigate this risk, but customer-supplied encryption always will because the customer knows where the dividing line stands.