Essentially, most top schools have a process that goes something like this: individuals are given scores based on the different dimensions of their application - stats, leadership, volunteering, research, clinical experience, etc. I have no idea what the categories actually are but I suspect they look something like that. Your interviewers will meet with you, write some comments, and score you based on your interview performance and overall application. After the interview, there are often multiple admissions committees that review and assess applicants in parallel. I believe at Harvard these are organized regionally (so, one adcom for the Northeast, one for Midwest, etc.). If an applicant is above a certain score threshold (meaning all aspects of their application are "good enough"), they are voted through and then assessed by a "master" admissions committee that is now considering the top applicants. This master adcom is then responsible for "crafting" the incoming class, so they select for certain characteristics that they might want - eg. a certain number of athletes, a certain number of research superstars, maybe engineers, or English majors, etc. and make sure that there is enough regional, as well as ethnic, cultural, and SES, etc. diversity.
So, even if everything in your app is solid and you make it past the preliminary adcom, you still might not be accepted just because the master adcom could find that someone else fits better into their ideal composition of the class. That, I think, largely explains why some applicants will get into some of the top 5/10/20/whatever schools but not others. Most people who have good applications and do well on their interviews likely make it past the sub-adcom. It's just the part after, at the master adcom, that the process becomes hazy and kind of random.