How would they know your the only one in the world?
Coz my mummy says so.

But in all seriousness, if you type my name into FB, there is only one listed. They could have course believe that it may not be me, but the chances are they will know it is. I mean, most people are on FB now. Same as my Linkedin.
Even if they are just small preview pics of past cached websites, they are still there......

