Aren't most Swift providers already using 2x-3x duplication? Putting parity on top of that would be like RAID15 (the reason you've never heard of RAID15 is that it would be crazy expensive).
Yes, swift provides multiple redundant copies of the data. It depends on what you are protecting against: failure of a piece of your data or failure of a hosting provider.
If you simply rely on "dumb disks" spread across multiple providers to provide availability, then you may be interested in looking at the nova-volumes part of openstack (it provides block storage attached to nova VMs). As part of openstack, it's an open system that is seeing rapid adoption.
However, one of the most-requested features for swift is to provide support for logical clusters that span a wide geographic area. This could potentially allow multiple providers to collaborate in providing a multi-provider storage system. However, I'd guess that the technical problems are much simpler than the business problems in setting up multi-provider clusters.
