I think that her comment may have been inappropriate because while she did not say a name, by saying 'cop killer', people knowing where she worked, etc...her comment was not really appropriate for facebook.
What people have to keep in mind, however, is their conduct on facebook, twitter, etc... I used facebook, but to play games, keep current with my alumni and astronomy associations, and I enjoy posting positive or thought provoking quotes for people to read and ponder. Outside of that...saying what mood I'm in, discussing work, etc, is not done because these people are not my friends. And, we have to also keep in mind that judgements are being made about our participation on these social networks. An example is I have a friend who is returning to school and when I note that she has posted her reward points for games at 3am, but I also know she is not doing too well in class, I assume that she is more on facebook than she has her face in her textbook. Now, it could very well be that she has studied for hours and facebook is an outlet.
We don't always know how people perceive us, so, we have to proceed in caution...even in our socialization. People violate our wishes to be 'tagged' and post your pics on facebook with no permission. I may have intended to go to that party, maybe already knew that a few people would take our pictures, but, I did not agree to have my face tagged and spliced all over facebook, myspace and twitter. Bottom line, the age of transparency is here...and people will take advantage of that in many ways to use against us.