To be fair, it should be "Know your rights, as well as the rights of others." as the article cites employers rightfully defending certain disciplinary actions against employees. In the first case in the article, the woman was either fired for poor performance or griping about her boss. If it was for performance, she deserves to be reprimanded in some way, but for griping they need to just leave it be as it's away from the work place. On the flip side, if she ever found out that her boss called her a "whiney little b!tch" on his own time away from work, she wouldn't have a right to complain either.
When it comes to the speed of change of the digital age, laws often have a slow response to the ever shifting landscape. It's best to remind yourself that even though you have rights, so does everyone else as well, and there will be times when their rights trump yours. Learn to avoid a problem rather than help create one.