Just because I'm not on Facebook (I'm not), anyone that's allowed Facebook to see their own contacts, in their phone or email, has shown that they are or are not connected to me in some way. Without me actually ever even having an account with Facebook they can correlate this data from users to see who is likely to know one another by a shared connection to me. Just because my particular node on the relationship tree has more blanks than it would if I was a Facebook user does not mean I don't create a node at all.
My guess for this Facebook issue in particular is that the Doc potentially did absolutely nothing herself, but rather all of her patients had mail and phone contact lists that included her and that common thread along with the same geographic area was enough to trigger a recommended match. In other words, this was equally likely to happen even if the doctor never had a Facebook page of her own.