FaceBook sent a friend invite without my permission?

[Leo]

I logged into FaceBook today to find out that someone I knew (outside of college) had accepted my friend request. The thing is, I never sent the friend request in the first place. I checked with this person and they told me that just before the request was sent, they got a message saying, "Do you know Leo Ford?" to which they replied, Yes.

Apparently that gives FB permission to send them a friend request on my behalf.
During that time, all the friends of this person, could access my account.

What happened here and how do I stop it in future?
I checked my login sessions in FB's security panel. Only I have logged in recently.