The count terminates whether B2 gains PC or not.

Team A is in control of the ball in the BC, B2 knocks the ball away and you are terminating your BC count?

Also, let's not forget that the partner did know the BC exception in relation to this play: "In our post-game discussion, he says there's an exception in the BC rule for a steal." The defensive player did not steal a pass while airborne. The partner did not say that B2 never gained PC in her back court.

B knocked the ball into A's front court . . .

That's not the description bainsey gave. He said B2 stole the ball in A's back court, he didn't say she knocked it away.

No, otherwise it wouldn't have been a violation. The OP said they gained control in A's backcourt (B's frontcourt) and then went into A's frontcourt (B's backcourt). So the count wouldn't terminate until B gained possession, still in A's backcourt.

He called backcourt violation because Team B gained possession in its FC and then dribbled into B backcourt. Bainsey would have been counting 10 on team A originally. If B gains control of ball then the count on A stops. If B just knocks ball around then count on A continues until ball hits A FC.

He called violation so he had to have determined that B controlled ball in FC and dribbled or fumbled it into BC and was first touch.

B2 "took" the ball into B's BC. That terminates the count whether B2 has PC (as part of the "taking") or not.

B2 first touched the ball 3-5 feet from the division line. bainsey is responsible for the count. Until the ball moves to Team A's FC he has to judge whether or not B2 is in possession at any point before she crosses the division line. He so judged. The same way it could be judged Buddy Hield had PC in his front court in that play from the Oklahoma game (absent other aspects of that particular play).

I think BNR's point is that since Bainsey was the one on ball here up until the steal, this particular call is actually easier for him to make.

I think we can agree that at the beginning of pressing action, the job of judging BC violations belongs to new L. That's one of the reasons that L stays back to help on the press. (And, the same applies to C in three-person -- and if it's really a strong press, it *might* even fall to L)

At some point it switches to new T.

In between, it might be some joint coverage.

As I envision the play (recognizing that I might be envisioning it wrong, after re-reading the entire thread; and recognizing that others might be envisioning it differently), I don't see it as being the new T's (full) responsibility, yet.

I think that this is one of those calls where either official can get it (assuming they both know the rules, of course, which was an issue in the OP). And, if one of them judges control and the other doesn't, ...