A quick clarification: Ahron Kotler is most certainly *not* the Rosh Yeshiva of BMG, or a member the Moetzes Gedolei HaTorah. He runs the business side of BMG (quite successfully), and the only yeshiva policies that he decides are the financial ones (hence the title of CEO). He’s a great guy, but he’s he’s a businessman, not a Rabbi – and I think he’d be at least as shocked as anybody else to hear somebody suggest otherwise. (Although perhaps not as shocked as some of the right-wingers of Lakewood, who don’t particularly like him.)
– From somebody who actually learnt in BMG, just relating the facts on the ground.
You haven’t said anything new. The Golden Rule states he who has the Gold makes the Rules. Although some grandchildren/in-law ended up with the title rosh yeshiva, only one person runs the yeshiva. Hence the head of the Yeshiva is HaRav HaGaon Aaron Kotler Shilitah, whether he gives a shiur or not.