Facebook is another modality of human speech. At first, we spoke and things lived in the minds of listeners alone, or to those to whom the words were related. Then, with writing, we could record words durably, and any who could read and had access to the text could know what we say. Now what we say is durable and trivially disseminated to thousands, perhaps millions.
By all means, speak your mind. But consider first if you want what you have to said known by all possible recipients of the speech, and if you're wiling to deal with all consequences thereof.
Edit: none of which is to say that forcing people to divulge passwords for or the content of social media for employment purposes is remotely ok. It's not.
If this classroom assistant had simply sent her funny photo to friends using e-mail, perhaps we would not be reading about it?
I do think some kind of privacy protection is needed, in Europe we have some laws, but they are not perfect.