This is true, but its preferable to me to have all my "friends" already friended with me rather than the impersonator. I don't think my way is the only way, I'm not going to tell anyone not to stay off fb, your method may well be more effective. Of course all my close friends know if I'm not facebook or not - but not my aunts and cousins and old highschool friends and coworkers and past buisness collegues ex girlfriends, ex girlfriend's mothers, neighbors etc.
What the impersonators often seem to do is find a buisness directory where you may work/have worked, create an account with your twitter profile picture or linked in picture, then try to friend everyone in that buisness and all their friends.
But if you're someone who doesn't have a tight friend circle, like, as I mentioned, a city councel member or buisness owner or a pastor - who will probably have a large part of their congregation want to friend them, its not possible to have a tight circle of friends. They'll juse see that pastor Dave is on facebook and wants to friend them - great - time to tone down the horny-posting.