IANAL but I would of thought giving someone else your Facebook password ( or any other credentials to a computer system) was actually against the law, under Computer Misuse act.
Your Facebook account is a set of credentials for your own use on a private companies service. Certainly it is a service that allows you to make information public, but the account and the equipment it runs on belong to a third party, and your access to it is at their discretion.
Giving your details to another person without the permission of Facebook would constitute you facilitating unauthorised access to Facebook's systems, and your prospective employers use of said credentials would be unauthorised access itself.
In fact (and even more IANAL here), isn't asking someone to commit a crime for you actually a crime of solicitation? Possibly even blackmail if the situation is actually "commit this crime or we won't employ you".
If I were asked to handover passwords to any systems the person asking did not own, be it a service like Facebook or a more private system, I would refuse to do so on the above grounds.