I'm sorry, but how is that relevant? I mean, why not ask for their password for their online bank account so you can make sure they aren't involved in illegal activities. Or ask to see my home computer so as to make sure I don't visit bad sites when online.
Plus, what's to prevent them from logging in and posting things to get me in trouble? If anything, they are just opening themselves up to something bad. I mean, they already get your Social Security number, generally a bank account number if you use direct deposit, and a lot of personal information. I mean, what if you had your parents on Facebook. Someone could figure out your mothers maiden name and other personal information like first pet's name, first school, high school mascot, etc that people use as passwords or at least, security questions.
Also, why can't they just view my profile like everyone else does? I've never had a friend say "I'll only be your friend if you let me surf your Facebook account." I mean, yes, some people post dumb things online like underage people posting pictures of them drinking (without parents around). But why would you place something bad on Facebook. And, if my employer isn't going to hire me cause I play Farmville or take pictures when I'm on vacation, then I really wonder.