Ken_vs_ryu has found a way to download torrent files directly to the PS3 without using a client.
Here are the instructions on downloading torrents directly to the PS3 via TorrentRelay, please use with caution and intelligence:
1. Find a torrent file link.
2. Copy .torrent link (ie: www.mininova.org/get/########)
3. Go to http://torrentrelay.com
4. Click on the 2nd input box with [Get URL] next to it, and type in the link from step #2.
5. Click on [Get URL].
6. Click on the file you want. It will list all the files available on the torrent.
7. Save As dialog should pop up.
8. We only tried an MP3, and it was downloaded directly into the Music folder. Video below:
Note: This really isn't good for the torrent community since the PS3 cannot seed files, but it's interesting that it's possible.