To T or Not to T, that is the Question

Had a game this past weekend, two schools playing at a neutral site. Timeout called. Teams come back out on the floor. "Home" team only has 4 players, and I was double-checking my count when partner went ahead and gave the "visiting" team the ball for the throw-in. I see the 5th player for "home" go to the table during the throw-in, and then lo and behold, she enters the game while the clock is running. I blow my whistle and give the T sign. When I went to report it, the timer, who is the AD at the "neutral" school, indicates that it was his fault because he told her to go ahead and enter. After conferring with my partner, I waved off the T, with explanation to both teams. Good handle or bad? How would you have handled it differently? I know one way I would have handled it differently would have been to hold partner up for a moment while I was double-checking the count, but he was wanting the pace of the game to go quicker because the teams were slow coming out of their timeouts.