In a follow up to the blog post from Google arguing against IP addresses being Personally Identifiable Information, I have a couple of more comments.
A couple of months ago we ran into the exact same issue. While Whitten does make valid points that a laptop user can move their IP address around (from home to the office to the cafe), there is another case. What about the home user that has a static IP address on their home server? Perhaps its reverse DNS is mail.homeuser.com or something like that. In that case, their IP address would not be subject to change and therefore you could, quite conceivably, learn their identity.
That seems to be the situation that the EU is targeting. I don't really agree with it since it only identifies a machine and not a user. A home PC can be infected with malware that sends out spam. Somebody other than the traditional user could be browsing to a web site. However, the question is a legal one and not a technical one. Of course, if it were a technical question, it still wouldn't provide absolute proof of identity, it only suggests it.