End of Game Situation

[BigGref]

This didn't happen to me, but I was just thinking too hard over Thanksgiving when I was looking through the case book (NFHS).

If regulation ends tied A-55 B-55, and slightly after time expires an A player or coach says something inappropriate that gets him/her a T. As you are getting ready to administer 2 FTs to B1, the scorer buzzes you over to tell you that there was a scorer's error 1 point in favor of the a) A team, or b)B team. What would you do?

Some of the principles that I know/{or think I know} are the following (in which some contradict the others);

An OT officially starts with Jump Ball, or in Disposing the ball to a team in OT.
So, has the OT period started? Will it be unneccesary for B to shoot the shots if they were already ahead before the "official" start of OT(as in situation b) )?

Open for comments/thoughts/debate about a) and b)