The kid making that choice certainly believes that Chicago offers something different from HYPS. Other kids will make other choices, and, yes, some kids will end up at Chicago and be happy there after being rebuffed by a preferred school. These kids are also okay in my book, and there’s hope for them too. Just let them not be the dominant majority.
Interestingly, the kids at Harvard and Stanford in the study you cite also think that Chicago offers something different from their schools and other top schools. They preferred what their own schools offered - greater prestige, greater social life, etc - and they feel Chicago doesn’t have enough of all that, but they were in no doubt about what it does have - that purer focus on studies and even a somewhat “scary” intellectualism. That’s the brand. It is not a large leap of logic to assume that the brand attracts a type and that the type reinforces the brand. We see evidence of this constantly on cc.