The kid's safe; end of story. Nothing requires the PU to announce "Play" after every dead ball. Likewise, nothing requires him to call "Time" for every dead ball.
Under OBR 5.09(e), "The ball becomes dead . . . when a foul ball is not caught; runners return. THE UMPIRE SHALL NOT PUT THE BALL IN PLAY UNTIL ALL RUNNERS HAVE RETOUCHED THEIR BASES."
Simply stated, by allowing the pitcher to attempt a play and making a decision at the play at the plate, the umpire had already "put the ball in play". If it were not in play, the umpire would have (or should have) prevented the pitcher from either pitching or making the attempted play.
By usage, custom, interpretation and probably somewhere in the PBUC Manual, it states that the ball becomes live after a foul ball when the umpire determines that everyone is ready to play. (i.e. the runners have retouched their bases, the pitcher is on the rubber ready to pitch and the batter is in the box, the umps are ready, etc.). No verbalization of "Play" is required.
Jerry
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