Mistaken clock not starting error

[JugglingReferee]

Here's the sitch.

Near end of quarter, 3.6s left. Backcourt endline throw-in. Thrower-in bounce passes the ball to A2, who doens't touch the ball. I'm T, keep my arm raised and eye the clock, becasue as we know, many timers start the clock when they think the ball is touched, not when my arm comes down. So the ball is bouncing, as yet untouched inbounds, and my P, the R, with his back to the ball, sees that the clock is not running. He whistles it dead and tells me that the clock wasn't running. At the whistle, the ball was bouncing right at half-court, still untouched, and B has dropped down to a zone. After the whistle went, A2 picks up the ball, and my P turns around to see A2 has it.

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