Foul shots in the wrong basket

[JTRICE]

I would like to get basketball officials opinions on this senario. It appeared on our state basketball exam.

First quarter: Administrative technical foul on Team B. By accident the officials shoot the 2 Free throws at the wrong basket. A1 makes both shots. 2 points are added to team A's score.

Fourth quarter ends. Game tied. Team B coach calls the officials over and points out the error in the first quarter. He says that since the shots we administered at his basket, the 2 points should have been given to his team (Team B) and not to Team A (the team who shot the 2 Free throws into the wrong basket).

Official rules that:
1- It is a correctable error but that it is too late to correct.
2- Even though the shots went into Team B's basket they were shot by A1 and they count for Team A.
Game tied. Overtime will be played.

Is the official correct?