Not sure I'm qualified to weigh on this discussion, since I'm not quite sure how I got into Tuck myself. My numbers are good, but not mindblowing, and I felt like my interview was awful. I am a woman though and I work for a fairly blue-chip PE firm. I'm also a good writer, so even though I thought my Tuck essays were weak relative to my other applications, they were probably good relative to the others in the applicant pool.
I can't remember if Dartmouth asks on its application what other schools to which you're applying, but I think your answer to this questions matters to them. My understanding is that Tuck is SUPER concerned about yield so if you're a strong candidate and you're applying to a lot of great schools, adcom is probably concerned that they'll give you an admit only to be rejected for another top 10 school. After I attended their women's weekend in the fall, I really fell in love with the community so I sent Dawna and Pat (who's in charge of woman's recruiting) a thank you email for hosting us for the weekend and also expressed that Tuck was my top choice. It wasn't long or overdone - only a few sentences - but I let them know they were my number one choice. I also wove into my essays details that showed other experiences in my life were similar to what I wanted from my business school experience. In other words, for undergraduated I attended a small, private liberal arts school where there was a strong emphasis on community; I really enjoyed that, knew that I thrived in that type of environment and thus knew that Tuck, which has a similar feel, would be a good fit.
Only one aspect, of course, and just my speculation - just something I would consider as it shows that a ding doesn't mean you had a weak profile at all - could actually mean you were TOO competitive and they thought they would lose you to H/S/W.