I had a provider pop up on Facebook as a "suggested friend". I've had other people from my phone book pop up, people I barely know and haven't been in contact with for years, but obviously this is different. I've seen her a few times, but certainly don't know her RL details. Her work # is in my phone under an unrelated alias.  Could FB have pulled it from the number alone ? It freaked me out and I blocked her from coming up again. I don't want that information. (Luckily my wife wasn't looking at me when I turned pale ...)  

...Decline it. Facebook matches the phone numbers in your contacts to other people's contacts, and uses those matches to suggest them as friends

Keeping the wall between the two worlds is hard enough even without FB.

Probably 50% or so of the providers I see end up popping up on my Facebook "Do you know?" feed.  Sometimes, a couple of months after I stopped seeing them.

FB friends using our real names.  So far, no problems.  Our interactions have been strictly on a personal friendly  level.  Sorry, I can't help you on getting rid of her on FB.  When FB asks you if you want someone as a friend, and you do not want them as a friend, delete the friend request.

Thanks. It's seeing someone pop up when you don't know their RL identity that's weird. No friend request to decline, just big brother Suckerberg.
I appreciate the feedback, everyone. It's reassuring.

Also, its because FB uses your loction services to find friends nearby. A civvie friend of a friend tried it out at a work event and people that she did NOT share phone numbers/ info with popped up as suggested friends!

Oh woah. I did not know that. Man, FB is more than a little creepy sometimes.