Generally, safety deposit boxes are considered your property. However, renters in general have a property right in the space they rent, derived from landlord-tenant law. But that property right involves reciprocal rights, liabilities, and obligations. If a bank negligently causes loss of the contents of your safe deposit box, they can be held liable for that loss. When analogizing from safe deposit boxes to the cloud, as many have tried to do (including in legal cases), that whole element of reciprocal obligations is missing.

Do you have a property right in your Google Drive? Do you pay rent? Can you sue Google if they negligently lose the contents? Does Google have any obligations to give you say 30 days notice before they shut down your account? These reciprocal obligations are the difference between renting a garage to store your papers (which would fall within the 4th amendment), and simply leaving your papers in a friends' garage (which wouldn't).