Recent example: while I was logged out, they put my picture on their “quick login” page with a little red number “2” on my photo. Well gee, turns out there wasn’t “2” of anything in my profile to see: no unread messages, etc.; no, it was just made-up crap to make me want to go check Facebook again.
Not sure why Facebook is so desperate for attention that they need to LIE to get it but advertisers should be concerned: anything Facebook claims about “active users”, etc. is probably greatly exaggerated.