Here's my staircase analogy:
Your application is assessed and you are placed on a specific stair of a broad staircase (one with room for more than one person on each step -- imagine the US Capitol). Now the doors open and those at the top of the staircase are admitted for interview. After interview, you are assigned again to a step on the staircase roughly in the same positions as before but some may have moved up one step or more based on an excellent interview and some will have been demoted a step or even sent to the bottom step based on a very bad interview performance or rude behavior on interview day. Again, a door opens and those at the top of the interior staircase are invited to matriculate until a specific number of invites have been made (often two or more times the number of seats to be filled). Others are told to wait and a few, at the bottom of the staircase, and anyone still waiting outside at the end of interview season, will be told that they cannot be considered for admission (some schools will cut lose applicants who aren't going to qualify for interview at an even early point in the season.)
This is to say that your application on paper still holds some influence after interviews are over but you have the potential to rise to the top of the staircase after interview or you would not have been invited (unless your invitation was a courtesy due to your "VIP" status).