No. I once got a DMCA violation warning email from my ISP for downloading the complete Harry Potter series... which I hadn't downloaded. After a little digging I realized that I had connected to a torrent containing 1000+ books for less than 5 min the month before, and Potter was in it.
The publisher hired someone to watchdog torrents and record IP addresses, then sent out warnings to the relevant ISP. No lawsuit was involved, but if there had been I'd be bankrupt from either an out-of-court settlement or from court costs (and probably still would have lost).