My grandparents are from Chicago, but they retired to Searcy, AR in the late 70's or early '80s. As it were, I have been to the Harding University campus many times. My grandma (who was Catholic!) would take us for lunch in the cafeteria and we'd walk around the campus grounds. Searcy is a small town - not a lot to do there. As Xidelt and tcsparky mentioned, the school is operated by the Church of Christ and it is very conservative.
I always thought it a little odd that Harding wouldn't allow national GLOs, but would allow these social clubs which operate almost identically to GLOs. If I had to guess, I imagine that the church wouldn't be comfortable with the concepts of membership selection and not having knowledge, or control of, the GLO rituals. If I recall correctly, Harding's "recruitment" procedures include an "everyone gets a bid" type of format.
Edited to add a link from a previous discussion on Harding:
http://www.greekchat.com/gcforums/sh...ad.php?t=72480