Tor relies on the fact that even if there's one or two bad apples among the bunch logging everything you're probably going to be safe because you'll go through enough routing nodes that aren't logged for it to be impossible to trace.
If all you can see is routing you can't know where packets originate or are destined to. You receive a packet, open your layer of encryption, see where the packet should be going next, log it, and send it forward. You can't possibly know whether the sender created the packet or forwarded it, and you can't possibly know whether the recipient consumed the packet or forwarded it.
You would need to monitor physical network links to determine patterns how the onion style packets travel around.
Someone already attempted to make something similar to what you're describing, but it turns out that it's very hard to do right.
Translated to BitTorrent, everyone would be using just one extra hop to keep the speeds up but passing around encrypted packages for others would create plausible deniability. You can claim you don't know what the packet that you routed contained, because you can't know that. You can't be held liable for routing traffic per se, much like ISPs aren't liable for routing traffic per se.
Why Tor and I2P don't want to use one-hop connections is that someone with government-level access could deduce the participants by looking at the traffic timing patterns. But MAFIAA at least not yet isn't actively hooked to the major ISPs of the world and can't apply such a traffic analysis. A simple one-layer indirection would hide who's downloading and uploading what. All you see is routing nodes.
If you're MAFIAA and seeding your fake movies and music to this torrent network, you can only see a user's IP address uploading a block to your fake clients. But since everyone is acting on behalf of others and merely routing packets, you don't know who sent the packet and you can't possibly prove that the one who did the last route was guilty. Otherwise merely connecting to the network would mean the user is guilty. The network would of course transfer legitimate files as well, and while downloading a Ubuntu 13.04 image users would also handle these one-hop routing requests of other peers who are downloading/seeding other files.
Interestingly, you would only need to transfer a certain percentage of connections over the one-hop tunnel. You could use zero-hop for the rest. The MAFIAA can't recognize those so it still looks the same as if you acted as the router and fetched a block for another peer.
This could also be implemented as a global free-to-connect IPv6 VPN network. If the IP addresses uploading MAFIAA movies are virtual, nobody knows where they are and who operates them.