Leigh Lewis, superintendent of the Triad district, told me that if a student refuses to cooperate, the district could presumably press criminal charges.
The school district aren't saying that the law gives them the power to compel students to give them their passwords. It also doesn't suggest that refusing to give the password is breaking the law. The school can ask, just as I could walk up to someone in the street and say they need to give me £5 or I will report them to the police for "being a moron", but as long as I don't threaten them, stray into harassment territory or impersonate a police officer (or other protected role).
That doesn't mean that the schools don't deserve to be chastised for sending out threatening, intentionally technical and misleading letters though.