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I believe fielders choice is defined as; an act of a fielder upon receiving a batted ball, chooses to put out one runner, and allows other runner/s to advance to another base. In the example you metioned the pitcher allowed the batter to advance to 1st but did not get an out. So the scoring would either be batter reached on a base hit, or reached on the pitchers error. I do not believe this to be a base hit.
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