First of all, while it does look like he did actually shoplift, two anonymous sources do not make this an open and shut case. That alone means that there is a small chance Boeheim could be further punishing an innocent kid. Jim has to balance the effectiveness and appropriateness of the punishment with the trust he could lose for not believing MCW.
Assuming the sources are credible, which is likely, he already served a punishment that fit the crime. A college kid paying $500 hurts a lot more than missing a game against some OOC cupcake. I don't really see the point in Boeheim adding onto a punishment that seems sufficient.
As for the media and our school's reputation; screw 'em. Do we really care what they think? I doubt it will impact recruiting much. Jim is an excellent recruiter and a few bad stories aren't going to drive prospects away. If they do, then those are recruits we probably wouldn't want in the first place.