In many European countries they can. They set up honey pots, log everything and then send costly C&Ds to thousands of people. Courts usually believe their "proof", no matter how bad it is.
I'd expect the honey pots to require at least consent before incriminating someone. Successfully incriminating people based on an action that the "damaged" party forced them to do without even their consentiment is a bit too much to expect.
But then, I'm not completely insane. Laws often are.
Earlier this week, Prenda faced a new and serious allegation: that it had actually put some pornography on BitTorrent itself, intending for it to be downloaded so that it could start a campaign of lawsuits and threat letters.
The Pirate Bay gave the data to TorrentFreak, which says that the IP address 75.72.88.156, which uploaded some porn files that Prenda has litigated over, "was previously used by someone with access to John Steele’s GoDaddy account."
It's probably a billion dollar business by now.