I wonder if what is happening is that Facebook often "suggests" to people that they should "Friend" mutual friends. If you don't look carefully it looks like they are asking to friend you and you are accepting their request but to them it seems that you are the one asking asking...
YES! I fell for this once when I first joined Facebook. And I felt like a moron.
Facebook suggested that I knew this guy John. We'd gone to college together, I hardly knew him, but I had dated his best friend. I thought John was sending me a friend request. At that time, the exboyfriend was not on Facebook and I figured there was no harm in accepting the friend request.
A few hours later, I got a private message from John saying "How do we know each other exactly?" And I thought to myself "He's the one who sent me the request. Underneath my name it shows that my network is our alma mater. Why is he asking me this question?" I wrote him back and mentioned college and mentioned his fraternity, but I didn't mention my exboyfriend.
John wrote back again something, I can't remember what. After several messages between us where he seemed kinda stand offish, I realized that *I* had been the one who had sent him the friend request. I felt like a heel. But at this point, I guess I had convinced him of my worthiness and he had accepted my friend request!
I was too embarrassed to tell him what had happened at that point. But after that, I tried really hard not to click on any buttons that looked like I might be adding a friend. And if I accidentally do, I quickly try to revoke the friend request. I think you can "un-invite" someone to be your friend if you catch it quickly enough.