Why seed a torrent day and night, linking your actual IP to the infringement act, when you can just upload a file to a bunch of file sharing services on a cafe's wifi and post a link on a forum? If your goal is to illegally distribute files without getting caught, real P2P seems like a suboptimal choice for now.
I don't know of a single VPN service that doesnt keep logs, they might not log the sites you visit but they all log which customer has which IP at which time.
I trust my VPN-provider when I ask them explicitly if they keep _any_ logs at all, and they reply no. They are not required to do so by law (yet, at least), where I live.