The theory goes that at the very top boarding schools there are so many qualified students, many of whom are hooked in some way (e.g. sports, legacy), that for many very qualified students it is very hard to stand out among their peers and that (another theory) highly selective colleges and universities will only accept a limited number of students from any given boarding school so there may be some students who might have received acceptances from their LPS or a good but not tippy-top boarding school where they would likely have stood out.