Can teachers and school administration access your Facebook profile if you are on their network?

[The Source]

I go to a small private school and some people think that teachers and principals and people can access your Facebook account if you are on their network. They also say that college applicants' and job applicants' Facebooks can be checked by the colleges and the employers. Are any of these claims true, because it seems like a serious breach of privacy?

My Facebook profile is on private, and nobody can see anything unless they are my friend first.