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.
In the end degrees come down to school prestige and/or what you make of the diploma. Individual school rankings(ie architecture, law etc) will likely remain unaffected but overall the degree will be worth a little less.