What about reading through your gmail/hotmail/etc. emails?

IMHO the fair game is whatever a FB user has visible to everyone. Everything that is limited to friends is private and shouldn't be employer's concern unless there are specific requirements like for clearance jobs. Also, login into your profile also opens your friends potentially private info and exposes it w/o their consent. IIRC, anyone can refuse answering a background investigator; the above bypasses such option.

I would have no problems, and actually suggest and welcome opening my profile, or 'linking' with potential/current employer on professional networks like LinkedIn.