An applicant from my school 2 years ago was offered an interview 48 hours before the interview date across the country because someone had cancelled. It was one of their top choices and a top program, so they went for it and ended up ranking it number one and matched there.
I think we underestimate how important the interview is in this process. The program director at one of my aways said that in the applicant pool (this program gets ~500 apps) the top 5% are superstars and the bottom 20% can be for the most part screened out, but the middle 75% of applicants are very similar. So this is why it seems so random as far as who gets interviews, there are so many of us that are so similar. This means that the interview is where these applicants are able to differentiate themselves from their peers in both a good and a bad way.
just my $0.02 (and I'm just an applicant too, so what do I know)