"Active" mean "currently logged-in" not only registered on the board. As I type this, you can't see me in the "active" section and, the "dot" at the bottom-left of my post will not turn green, because I selected "invisible" in my profile.
Anyone can surf the boards while being invisible. Simply access the "Edit Options" page of your "User Control Panel". It`s the first option on top of the page.