Black eye for the University. If they want it back they will need to bring the Medical Center back under their umbrella, they will also get a boost from the CIC. The real problem is that the university is comprehensive and balkanize, also most of their research money comes from the usda(which the AAU doesnt count) so they will need to look at other ways of bringing in research dollars.
I went to a private Christian college (now a university) so the AAU wasn't even on my radar screen some 50 years ago. I'm still only tangentially aware of the organization. Is AAU membership really that important to a university in terms of prestige?
It does seem that since UNL was among the very earliest of members, getting kicked out is, as you indicated, a black eye even with the caveats of the source of their research funding and the separate medical facility.
Yes, bring back the med school and NIH funding with it. USDA overhead is only about 23% or so, while NIH, EPA, and others pay the full 50% or thereabouts. It is all about research funding and overhead dollars.