Is there privacy online?

In a recent article provided for me by "A Schwartzenegger Republican" states that the Mayor of Spokane Washington is under investigation for speaking in gay chatrooms online. I believe that one of the key principles about the Internet we learned in class that anything someone puts online is for the public. We were taught in the first class that if you don't want anyone knowing who you are you must use an alias when blogging. To remain private we must not give too much information. I believe that if the Mayor spoke in this chatroom online and revealed his identity then his conversations in a public chatroom are for the public. He not claim privacy if he is unveiling his identity.