That *is* their business model.
I read up on this yesterday (German Language) and the situation is more complicated than it seems.
The providers affected are all over Germany, so various local courts were involved. The one in Köln really screwed things up: what the people are supposed to have done is Downloaded the file(s), what they were accused of was Sharing them and Köln went along with this. The difference is that the provider does not have to give out addresses on Downloads but they do if Sharing is involved. The actual "Abmahnung" letters which went out said nothing about Sharing at all. The Law Firm based their claim on the Downloads being in Cache so they were available for others. To make things worse, the largest provider in Germany (T-Online) is based in Köln. Other courts rejected that argument, others asked questions and the Lawyers withdrew their request.
I have a related problem at the moment - a couple of years ago someone accused me of sharing some other porno film, again T-Online was involved. My wlan is wpa2 with a 63-byte random, generated mixed upper/lower string and it accepts only one Mac address, I have checked both PCs which were on at the time for Trojans / Virii with a bootable scanner and there was nothing. Under German law there is no redress - if they claim it then I must have done it. I'm fighting this one out at the moment.
For me this is a reason not to use T-Online. My main account is now somewhere else but I *need* Internet for when I work at home and two independent providers (Cable and DSL) made sense back when the Cable provider was unreliable. I think I'm going to have to dump T-Online which means dumping Telekom for my phone.