Redundancy - by definition - cannot be supplied by a single company.
Yes, your vendor may have their own redundant systems in place so that their internal problems don't become your problems. And that's nice. They should. But you always have a Plan B. And you always keep a local copy.
What I'm saying is that whatever is in the contract is what matters. Data hosting, web hosting, data storage, whatever terms are used matter little.
EDIT: Case in point: We probably all agree that dropbox could be called "data storage", but they specifically say that backups and backup costs are to be done by the client (http://www.dropbox.com/dmca#terms), not by them.