A friend of mine in Germany also got such a letter once and wrote something back along the lines of "Wasn't me, don't know what you are talking about" and he never heard from them again.
They try to profit from the fear of everyday people who rather pay up front, because they don't want to risk that the case goes to court, no matter how unlikely this might be. And it's even understandable, ordinary folks probably really panic when they see such a letter and all the legal talk and underlying threats that are made.
It's as despicable as patent trolling.
First avoid such a situation:
-) use vpn if possible (check with their policies, whether they allow torrent traffic or maybe they ban it from certain servers, preferably use a provider that does not log)
-) quite simply never download newer material with big companies behind them from public trackers. most of the times these letters regard the newest Hollywood movies, a current album by a big pop star or the newest game everyone has been waiting for, not Taxi Driver, The Godfather Trilogy, Quake 3 or the weird Japanese pop band from the 80s you are into
and if you are in such a situation:
-) consult your lawyer or search on the Internet how to properly respond, do not just pay!