You can choose your settings on facebook so that your profile is open to just "friends", just your "network" (usually geographical, i.e. your home town, but could still include thousands of people you don't know), or everyone on facebook. Er ...apparently.
My own personal feeling is if that you're too stoopid to manage your privacy on a site a simple as facebook, you're probably too stoopid for the RAF to want you. Or Oxbridge, for that matter, which is probably why they're so enraged.