I think what got the heebies jeebies scared out of DN is stuff like the ruling made by Austalia's court in which Australia's version of the MPAA was able to hold not just the owner of box, but his ISP legally liable for merely providing a link to box by the reasoning that anyone who helps with piracy is responsible for it. See here:
http://yro.slashdot.org/article.pl?sid=06/12/19/0521206
Now you might argue that currently this is only occuring at the ISP level, but I say just give it time and the problem will go up the chain a bit more. Look at what happened with Research In Motion and the BlackBerry lawsuit. A Canadian company got nailed hard in U.S. courts by a bunch of patent trolls showing that screwing is an international thing. I doubt DN wants to be caught on the wrong side of CP investigation by some sort of government investigation (be it Danish or anyone else).
Registrars shouldn't need to worry about this, but the key word in that statement is "shouldn't." Currently DN "shouldn't" need to be part of any investigation (since that's the job of three letter agencies) or involved in any corrective action that is taking place, but, as both the Australia ruling and RIM case prove, exactly who is responsible for what and to what extent the international boundary stops is a very dangerous question. My thoughts on the matter is that DN took a very active action in the matter to cover its ass accordingly since CP is a more dangerous thing to be dealing with than any piracy as the definition of it is pretty much international and the liability for it is something that no one wants.