what you are talking about is the AAU - not amatuer athletics but the American Association of Universities. Traditionally, the B10 and P10 were AAU schools that played major college football. AAU member schools was a main dividing line between the P10 and B10 and the other D1 football conferences. The screw up was that Nebraska, which had long been in the AAU though not in the B10 or P10, got bounced from the AAU in 2011 *after* they had been invited to the B10, leaving some folks with egg on their faces. AFAIK Nebraska still hasn't gotten back in but supposedly is working on it.