Clock/Time question

[tigertater]

Hoping I can get some clarification on this one, as this has caused some rather heated discussions at our training meetings......this is one of the true/false questions on a rules test we are looking at.

A1 is fouled in the act of shooting just prior to the horn sounding to signal the end of the quarter. A1 is placed on the free throw line with 0:00 showing on the clock and no other players in the lane. (T or F)

At our camps over the summer, this situation was discussed, and we were told that with foul taking place with time on the clock (clock ran out due to lag time between when the whistle was blown the the timer could react to the sound), that some amount of time should be placed back on the clock, and A1 would then attempt the free throws with players in the lane.

This makes sense - however, no one can find anything in the NFSH books stating that time should be placed back on the clock..........and this is where the discussions get heated. If in fact what we were told at camp is correct about time being placed back on the clock, what ground would the officials have to stand on in this situation if it were to happen and the coach pulled out a rule book and asked to be shown where this were located?

Thanks in advance.