After reading the case play, I would have to agree. Take the erroneously awarded FT off the board and resume the game with B's FTs.
Isn't it interesting though, that if the error had been a failure to award A1 his FTs, we would go back and do it. Yet, if A should have gotten the ball instead, as in this play, we don't give it to them. That's an inequity if there's ever been one.
I'll say it again! I hate these things!