Clarification on when a Coutesy Runner may enter the game

[Banjo26]

Looking for a little clarification. During a recent 16U tournament held under ASA rules, our team used a substitute player as a Courtesy Runner for the Catcher after she reached base. Once the inning was over, we tried to enter the Courtesy Runner/Substitute into the next defensive half inning for an outfielder and the umpires determined that she was not allowed to enter the game until the defensive inning was completed citing Rule 8, Section 10(d). Is this a correct interpretation of 10(d)?

Thanking you in advance.

[UmpSteve]

I believe the rule requires no interpretation.

A player may not be a substitute for any other player in the half inning that they participated as a courtesy runner.

The next defensive half inning isn't THAT half inning.

[Banjo26]

Wish you were in Colorado! Thanks.

[UmpSteve]

Wish you were in Colorado! Thanks.

I was. Apparently not on that field that day; I do Fireworks in Aurora, last 7 years.