It does not matter that the batter unintentionally made contact with it causing it to go out of play.
If we had a play at third and a thrown ball hit a sliding runner instead of being caught by the 3B, and then deflected into DBT, we still have a thrown ball out of play. This is no different, except it started as a pitched ball, and it remains, a pitched ball until it becomes either batted or thrown.
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