I've also read somewhere that the RIAA and MPAA (the USA recording and movie trade groups) can trace Torrent downloads. Personally I doubt it but who knows?
They actually can, by attaching so called "tracker" to the file.
My friend recently received an email from Comcast about copyright violation.
They listed exact torrent, file name, date, etc.
I assume some company attached a tracker to the file in question, and then, they complained to Comcast.