Ok, let's pretend the solution is technically possible across all potential end systems, and fantasize that the privacy aspect can somehow be handled securely.
Does Tiziano Motti have a disk drive or tape manufacturing company based in his home town? Never mind explaining how the key can be stored by the user; who's storing all that traffic detail, on what, and who bought all that equipment? It might be inexpensive to operate (it wouldn't be really, but theoretically it could be), but what about to buy and install?
If the system were just going to store hashes, then I expect the sites they are worried about would install something to regularly modify their content enough to change the hash values. Somebody will need a permanent record of what the content actually looked like at the time of the download, so he's not just going to back up the internet, he's going to retain regular backup snapshots for months. Or did I miss a detail?