[just another ref]

Originally Posted by Nevadaref

Time may have expired in the period, but there may still be game activity to be completed.
For example, a player may have been fouled while attempting a try and time expired while the try was in flight. We now have a situation in which a player will attempt FTs after the expiration of time in the quarter. The score may be tied or this team may be trailing (the game would be over if this team is ahead), but as long as the score is close enough for the FTs to possibly make a difference in the outcome they must be attempted. The outcome of the FTs will determine whether there is another period of play.

I am educated. I had always read this to say the end of the period, as opposed to the expiration of time in the period.

The opposing coach may wish to take a time-out in an attempt to "ice" this shooter. The rule is in place to prevent that coach from taking multiple time-outs in a row to really "freeze" this shooter.

Is this your theory, (I can't think of another) or is this published somewhere?
A coach would rather use multiple time-outs here than save them for use in a potential next period where they might be crucial? Seems unlikely.