[RefCT]

Maybe they were thinking it was a substitute and using 10.2.2. If you look at the Casebook, it says you have until the next live ball following the first dead ball to administer the T.

I wouldn't think this applies thought since the situation is "During a live ball and with the clock running, substitute A6 enters the court". I believe you said the sub was on when the ball became live.

I am not saying they were right and this applies to your situation. I am just giving you a scenario where they would be correct if the situation matched.

Edit - This was the justification on the 2014 IAABO refresher exam for question #33 which asked "Substitute B-6 enters the court while the live ball is in control of Team A and the clock is running. The officials are unaware that Team B has 6 players in the game. B-6 returns to the bench after which Team A requests and is granted a time-out. The scorer now informs the officials that Team B had 6 players on the court. The Referee rules the statute of limitations to penalize has expired. Is the official correct? ". I specifically remember this because I was surprised they said we could use the table for more information.