Wow! Congratulations!
Yale has had quite a bit controversy with many continuing to claim that it is not a truly Top 10 school, which to their satisfaction, Yale did get booted out this year from US News to spot 11. In any case, many believe that SOM's popularity comes from its high undergrad ranking and that BSchool is not as strong.... that's what I have been hearing over and over from Yale haters (in line with your references). I think in part the feeling is somewhat negative is that you would be attending the lowest ranking Yale school (Yale undergrad, ranked #3, Law - ranked #1, Med School - ranked #11, and BSchool - ranked #11), meaning the undergrads would probably be going to higher-ranking Bschools in 5 years. Some folks may feel as though the school is helped by the undergrad clout and carries the MBA name further, and to those who don't like to ask for help, it may be rubbing them the wrong way.
Yale does have a stronger international brand than many other Schools and it does attract more people since Booth, Kellogg or even Wharton are not as well known as Harvard/MIT/Yale. I think there is some exploration that will need to happen - take a look at the
Yale and Tuck reviews and see if you can spot any patterns. It is a tough call, but neither is the wrong solution if you don't have to pay for any of it!
P.S. Thank you for keeping the schools updated on your profile!