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Actually, Chuck, you don't need an out for an FC. You need an attempt at a different base, where the scorer can safely assume a play on the batter would have been an out.
For instance - runner on 3rd, no outs, infield back. Routine grounder to the pitcher. Pitcher fires home, but the runner is alert and beats the throw back to third. There is no out, but this is a fielder's choice (and yes - an at bat with no hit, so a detriment to the batter's batting average), assuming the scorer assumes the batter would have been out had the play gone to 1B.
On the bunt play - if there were no runners on base, you'd have scored this a single without thought - there's no difference. Base hit.
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