I agree Facebook probably keeps your information that you "delete". After all, when you leave Facebook all it does is deactivate your account - I have friends that have left for a year or two and when they come back they pop up in my friends list without me having to do anything. Obviously nothing was ever deleted.
What's more, I know that Facebook and Linkedin are sharing data. I do not have anyone I have a professional relationship with as a Facebook friend, but I do have a handful of Facebook friends who I'm connected with on Linkedin despite a total lack of any overlap in our careers or workplaces. It is really creepy that Facebook will make friend suggestions for me with people I work with (but am not connected with on Linkedin) with whom I have zero mutual friends on Facebook - in fact probably would have to go through several layers of friends of friends, Kevin Bacon style, to get to them!
This is only possible if Facebook is sharing data with Linkedin to be able to make that association between those people and people I'm connected with, and connecting it with my Facebook identity. (It isn't cookies, I'm very careful about clearing those and hardly ever login to Facebook other than mobile anyway and when I do it is in a private window)