SAD did indeed have family ties in Chicago.
Recall that Madelyn Dunham’s brother, Charles Payne, was assistant library director at the University of Chicago.
http://news.bbc.co.uk/2/hi/americas/8083967.stm
Your link shows the Charles Payne has lived in Chicago and worked @ UC, possibly all the way back to 1959-1960, when Ann would have been applying to college, so that solves the mystery of why she would apply there.
As I am uncertain as to if Ann Dunham is really Madeline Payne’s daughter, based on discrepancies from Janny Scott’s book ‘A Singular Woman’, I am leaning towards that the whole Ann & ‘Black Orpheus’ episode in Chicago is completely made up.
Your link also might imply a strong relationship between Charles Payne & Bill Ayers (UC - where Charles worked - is about a mile from Barry & Bill’s current houses) and this is probably how Charles survived the Obama Family Tree ‘pruning’.