This could be built out as a service that is competitive to SendFile, DropBox and other file sharing services. If I understand it correctly the server between the sender and receiver never stores the file itself which is unique.
EDIT: As a solution that doesn't need apps and uses the server only as a temporary middleman instead of actually storing the file, there's JetBytes[2].
[1]: http://www.getshareapp.com/
[2]: http://jetbytes.com/
But one problem is still remaining, and the present solutions are under the heaviest attack: discovery. BitTorrent is using trackers, and we've seen attacks on sites like PirateBay that provide those services. Is there a way to develop -- or perhaps it's been done already -- a discovery and tracking system which is truly P2P and simply cannot be attacked, at least not in a technical way?