I am Italian, living in Italy.
In 2007 I visited Vietnam with my then wife; our guide for the northern part of the country was a nice young lady who worked at Hanoi university and was incredibly fluent in Italian, having studied in my country some time before. We had no common acquaintances in Italy or anywhere else, and I have never been in the Italian city where she studied.
I did not have a FB acount back then, and opened it a couple of years later. After a couple of month, i get a friend suggestion for the lady, whom I actually had almost forgot. I asked her friendship, which she accepted, and noticed we had no other friend in common; in addition, I was her only Italian friend on FB.
I was impressed and a little frightened. It was one of the reasons I closed my FB account few months later, and never opened a new one.
Edit: I did not have any record of the lady's name, email, phone number or address before FB' suggestion, so it may have not inferred any connection from them.