across the Internet ... doesn't require storing data twice

A flavor of the CAP theorem applies here; if you want your data to be available even during network partitions (and those are going to happen on the Internet!) then it has to be duplicated somehow. For example, I still have a soft spot for Tahoe-LAFS, which allows users to control how much duplication will be used and typically is configured to have some redundancy. Typical cloud providers build redundancy into their storage products; for example, it's known that Google's Colossus storage system uses Reed-Solomon to trade space for durability.