So I shouldn't write letters to friends? Sorry, that's not gonna happen.
My personal facebook account is also my personal e-mail account. No one has the right to access it but me. If my employer has some burning need to see what's going on publicly on my facebook account, he's welcome to peruse the internet and see what is visible. He has no right to access what is not publicly visible (which is the only reason they'd need the password).
Hubby's company abandoned random testing ages ago because it violates individual rights. The industry standard now is screening upon hire, and access screening for particular companies, high profile, or high risk jobs, as well as drug and alcohol testing if an accident occurs. No more 'random' tests.