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For what it's worth ... here's what wikipedia says about baseball scoring of a rundown ... "if the defense allows the runner to advance to the next base in order (e.g., second base to third base), then the defense is charged with an error[SUP][citation needed][/SUP]."
Aside from the "citation needed" issue, it doesn't say who to charge the error too. But if is an error, it only makes sense to me that you would have to charge 3B because she threw the ball (thereby allowing the runner to reverse direction) when no one was covering the lead base ahead of the runner (3B in this case).
I'm sticking with that until someone proves differently!
Doesn't seem right to me that she should get charged with the error as she did her part.