correctable error?

[RoyalsCoach]

40 seconds to go. Our team has a throwin, backcourt on the baseline. The other team is pressing in the backcourt. The ball crosses half court around the 8 second count at which point the timer finally starts the clock. The ball is immediately knocked out of bounds. Now, I know as an assistant and I have no status but I could not help myself and said to the official that the clock did not start properly and why is this not a correctable error? The official replied, "because I am not the timer". He administered the throwin and the game went on.

My question is this? If one of the officials had looked at the clock prior to the baseline throwin and had definite knowledge of the time left on the clock, I am pretty sure from prior threads that you could use the timing of the 10 second count as definite knowledge to reset the clock. Is this correct?

Second part. What if the ball crosses half court and is dribbled several times before going out of bounds. If the clock was started as the ball crossed half court the clock may run from 40 to 36. Unless the official glanced up right when the clock started they will not know when the clocked started exacty. They will have definite knowledge that at least 8 seconds should have run off because that is what they chopped on the 10 second count. Would you run off 4 more seconds? More because there was dribbling after it crossed the half court? Or run none because you do not have definite knowledge of the exact time? Seems like in fairness some should be run off.