In the OP sit. the throw-in was not tipped by B...so no BC by A.
This exact play was recently highlighted on the website 60 Seconds on Officiating.
http://www.ref.60.com/
Referencing NFHS 4-4; 4-13; 7.6.2 and 9.9 they do a short review on
Throw-ins and the Division Line:
"It is critical to remember 2 key components of a throw in:
1.There is no team control during a throw-in.
2.A throw-in ends when the ball is released and legally touches or is touched by another player (inbounds or out of bounds).
This means that during a throw-in, any player may catch the ball in mid-air and land in his/her backcourt without committing a backcourt violation. However, if the released ball is deflected by any player, the deflection would end the throw-in and any mid-air catch by any player and backcourt landing would be a violation, if the player leaped from his/her frontcourt."