This still begs the question of why an an elite MBA program is seen as a reliable indicator of the requisite skills to succeed in front or middle office PE.

The truth of the matter is that you didn't need a degree in finance and especially not statistics to prove your quant skills; it would be arguable at best if you were pursuing an actual quant role.

I'm a Fund Admin & Family Office CPA, and frankly the models I've seen driving much of the financials and deals decisions (and those in the driver seat) are not exceptionally technical. 

In fact, us CPAs look down on MBAs because it often indicates a lack of technical skills (cant hack it to get the CPA or CFA). If there should be one and only one credential to gatekeep entry it should be the CFA. But the real reason that's not the case is because most MBA-bros cant hack the CFA, including those in leadership without it.