I believe you have it laid out correctly. In wrestling, the only way to get first is not to lose at all. The only way to get 2nd, is only to lose in the finals against 1st. Once you have sustained your 1st loss of a tournament, you then go to the "backside" of the bracket. If you do not lose anymore matches on the "backside", you take 3rd. Unless the tournament is placing 5th & 6th place, once you have lost your second match, you are done with the tournament.

Occassionally, at some of the national tournaments, the 3rd place wrestler will be given the opportunity to wrestle the 2nd place finisher - if he has not already lost to that wrestler at that tournament. They do not offer that option for KS State, or any of the regular KS tournaments as far as I know.