Answered: Clarification on T03

I am confused about T03 since it seems that it is applied differently at tournaments in my area. The rule states:

<T03> During matches, two teams from an alliance will play on the field. Any team which sits out
the first match in an elimination series, must play in the second match, with no exceptions. In
the third and any subsequent matches, any two of the three teams may play. Prior to each Elimination
Match, the Alliance Captain must let the referee know which two teams will be playing in the
upcoming match.

I read this to say that one of the teams on an alliance must only play one match in all of the quarterfinals, semifinals, and finals. So if a team plays in the quarterfinals, it does not have to play a match in the semis or finals. I was at a tournament this weekend where the judges interpreted this rule to mean that a team must play at least once in the quarterfinals, semifinals, and finals. Which is the correct interpretation?

This is the correct interpretation.