In this case they are wanting the students passwords to MySpace and Facebook even if they do not use at school. Getting the password means the school can then pose as the students and post as them and you could not prove students did not post. I understand the school and workplace has legal basis for saying what you can or cannot do when using a computer or network owned by the school or business, but they do not need passwords to see what people posted. Google and other search engines can get them to it. (as a warning that I tell my students, employers HR offices, and colleges admission offices will search and see what you have posted and turn down people for jobs and admission for information that is not a good reflection on them.
If I give you my Facebook password then no one can tell (including Facebook) that what you post to my account was not posted by me. If someone wanted to smear or libel someone and damage someone else, they would be to get the second person's Facebook/MySpace password and post the smear on the second person's MySpace/Facebook page and there is no trail to the real poster except thru some detailed computer forensics that may or may not lead to the true poster.
Would the school require all students who drive to give the school a copy of their car keys? Do they expect to have a key to every students home? Those are similar situations.