Wasn't it in the news a year or two ago about some state or city government somewhere actually asking you for all your account information (email address/password, FB address/password, etc) on all their applications? Too lazy to search right now, but I remember a huge uproar and they finally relented and changed their application.
With that being said, I'd simply refuse to comply if they "required" me to accept a friend notice as part of a background check. Oh, and you guys saying "You can grant them access without showing them anything" are technically right, but if you go that route, you're setting yourself up because I am sure the "background check" requires full access and if they find out you didn't give them full access (through a mutual friend, for example), they might use that as grounds for termination. It just isn't worth working for a place like that -- you are entitled to a personal life.
Also, I know I don't need to tell AT this, but I'll mention it anyway. I had hiring access in our system (a VERY popular third-party portal used by hundreds of big companies), and the functionality is built right into the system to conduct web searches on candidates as a "background" check. So beware.