Back door to an HBS / GsB alum

So, a few friends and I were recently having this conversation about how do some of the elite US based bschool fare abroad in terms of the reputation and prestige (yes this matters a lot in asia). Although I did not attend bschool, the schools my friends attended include Booth, Kellogg, Tuck, Berkeley, InsEad, Columbia and Sloan. The general consensus among us was that although these schools are truly elite and anyone whose a professional would have a high view of them, HBS or Stanford hands down are the most global and well known brand. Some, who already went to a top school, still seriously consider an advanced mgmt program from H or S a few years down the line if liquidity isn’t an issue. I’m Curious about the opinion that some of you have on this. Did you ever think this way? Know anyone who has? How did it work out?

PS - Let me also set the record straight on my perception of MBA admissions. It’s become a crapshoot process. A few years ago, certain type of profiles would have been guaranteed a slot at H/S (ex bankers, consultants, pe) Now it’s become competitive. But that’s not to say that a guy who attends booth / Kellogg / Columbia after 2/3 years of work experience wouldn’t have been able to get into H\S - assuming he got rejected first - if he had reapplied a couple of years later. Clearly he has the ability / fortitude / temperament to get into several elite programs and on the margin there isn’t a significant difference between these programs and the students they admit. But the rest of the world doesn’t know this