It is more than an internet rumor, but less than a requirement. IIRC, former Commissioner, Jim Delany, said as much at one point. Specifically, that AAU membership is preferred for potential B1G expansion candidates, but if a school brought other intangibles and benefits to the conference (hint: Notre Dame), lack of AAU membership would not restrict a school's ability to join the conference. So, technically, while not a requirement, I doubt there are many schools that are "special" enough to warrant an invite without AAU membership and it might only be ND.
Also, I cannot speak for all B1G alumni, but for those that I have spoken to, academic reputation is more important than football prowess when considering expansion. Things like AAU status matters and if it matters to deep pocketed alums, it matters to university presidents.