Yes, I agree Facebook Apps are often not your friends, but because they sell the data they mine off of you to spammers and the like.

This example is awful. That teacher is unprofessional, imho, if she was even friending her students. At all schools I have been to- It is against the rules for teachers to contact students for reasons other than school work related issues. No playing Xbox live with my awesome Art Teacher =/. But if I were that teacher, I would accept full responsibility for (1) Joining a Social Network and not knowing what I was getting into, and (2) Becoming friends with the people I teach and the consequences that follow