I was reading a booklet when I came across the phrase "personally identifiable". What does it mean in the following context (emphasis mine):
As the common household and business router will often display just one IP address for all of the people connected to it, the IP address will identify a group of people rather than just one individual. As a result, it is often hard, if not impossible, to be sure who exactly did what, purely on the basis of an IP address.
On the other hand, IP addresses are very often personally identifiable, and so, following a basic precautionary principle, must be treated as such unless they can definitively proven not to be.
First paragraph says that it's not easy ("often hard, if not impossible") to identify the exact person who did something behind a router shared with others. But "personally identifiable" in the second paragraph seem to say the opposite. I think I'm missing a nuance here.
Update: The booklet can be downloaded from http://www.edri.org/files/2012EDRiPapers/how_the_internet_works.pdf It does not define "personally identifiable".