You're all correct.
Of course we've reviewed everyone's files prior to arrival. Obviously we have to decide who we are interviewing and who not, and while I'm reviewing that I "score" each application.
The interview can move your score up, down, or remove you from the list altogether.
However, the actual day you interview has NOTHING to do with where you are listed. We let students choose the interview day that works best for their schedules. First day or last day, doesn't matter to me -- your position on my rank list = (quality of medical education) X (how well you did in med school) +/- interview factor + 10 slots up the rank list if you didn't wear black on the interview day.
Before someone flames me, that was a joke, and there isn't a real "formula". 😉