I disagree. False positives aren't intrinsically bad in and of themselves. What matters is how they handle those false positives. You're assuming that they'll handle them like the RIAA, but at this point there's no reason to assume it'll go that way except for cynicism and anti-corporatism. At this point, it seems that this company is trying to give people a fairer go, and that it's certainly a vast improvement over RIAA style tactics, so I'm willing to give them the benefit of the doubt.
I also disagree with the idea that this is similar to vigilantism. It's more similar to that software you can put on your mobile phone or laptop to trace it when it's stolen. While as a Pirate Party member I do feel there are fundamental problems with copyright as it's currently employed, in particular the length of copyrights, that doesn't change the fact that companies do have a right to protect their copyrights and their (intellectual) property. In fact, one could say they have a legal responsibility to protect their copyright as well. The fact is that if companies don't defend their copyrighted properties from these sort of things, it can be considered as legally the equivalent of them abandoning their ownership over it. No company, even one which thinks it could stand to gain from illegal downloads (ie. through word of mouth, goodwill, development of brand loyalty, etc), is willing to risk that.