A few random thoughts:

IPFS sounds a lot like what you want. Tahoe LAFS plays in this space a bit

The newer distributed file systems I've seen don't like permissions. They like cryptographically-backed capabilities. You have the permission to read the file because you have the ability to decrypt, through the key. (Of course, key management is easy </sarc>).

Some user-facing distributed filesystem talks drift into FUSE (or similar) territory. A TahoeLAFS dev talks about how users probably don't actually know what they want: https://plus.google.com/108313527900507320366/posts/ZrgdgLhV... (QUIBBLES: REAL FILESYSTEM VS. STORAGE APP section). This is probably less relevant for a package manager.

The first time I read about BitTorrent based deployment was from Facebook.