Interference?

[MD Longhorn]

Good point, Steve.

Let's assume, for the purpose of the argument, that absent the batter, the throw would have (in the judgement of the umpire) been caught by the pitcher and they would have gotten the runner out.

I'm not sure I agree with your "no longer has the right to occupy the batters box" comment. I don't see a rule to support that. The batter-runner is not required to be in any particular spot - we don't proscribe where she's allowed to run (well... running lane stuff, but that doesn't apply here). To me, this play does not differ from the following:

Runner on 2nd, BR walked and the ball gets away up the first base line a bit. Runner breaks, F2 retrieves the ball and throws to 3rd, striking BR as she proceeds up the line. That's not interference. Why would the OP be?

In every other case (running lane aside), we require intent to call an out when a thrown ball strikes a live runner (or batter-runner). Why would this play be any different?