B can get the TO if called before at A's disposal. On an administered throw-in, the concept is quite clear. When A gets ball from ref, ball is at disposal, count starts, B can't get a TO, etc.
I think that most refs look at the time where A is just getting the ball but cannot throw it in yet as a gray area, where they are inclined to grant a coach a timeout. Similarly, refs usually start the count when the player steps out with the ball and face the court, rather than when they first touch it. It is a matter of 1-2 seconds, but in my experience this is how refs handle throw-ins after a made basket. And if you haven't started your count (or normally would not have started your count), then you are treating B the same as you are treating A by granting the TO. Just my opinion, but backed up by many observations
I would also add that counts are not generally started until a player is ready to throw in unless the player seems to take excessive time. This observation is confined to the normal made basket, retrieve ball, step out, turn, and throw.
[Edited by Hawks Coach on May 15th, 2002 at 12:39 PM]