Interesting situation

[Nevadaref]

The action that the timer undertook was perfectly reasonable. If I were a game official, I wouldn't have any problem with it. The HC was making a time-out request at a proper time and deserved to have it granted.

Please note that the HC can go to the table and request a time-out any time that he wishes and challenge a situation as a correctable error or a scoring or timing mistake. When the HC makes such a request the timer/scorer is to signal the officials as soon as that team is in control of the ball or the ball next becomes dead.
If the HC is incorrect about the error, his team gets charged with a time-out and they are permitted to utilize any remaining time after the determination regarding the error is made.
So all that the HC had to say in the situation presented by the OP is that he asked the table for a time-out because he could not get that attention of any of the game officials and that he thought that there might have been a timing (or other) error. At the point when an official comes over he just agrees that there wasn't an error and gets charged with the time-out, which is what he wanted.

2-11-3 The scorer shall: . . . Signal the officials by using the game horn or a sounding device
unlike that used by the referee and umpire(s). This may be used immediately if,
or as soon as, the ball is dead or is in control of the offending team.

5-8-4 . . . Responds to the scorer’s signal to grant a coach’s request that a
correctable error, as in 2-10, or a timing, scoring or alternating-possession
mistake be prevented or rectified. The appeal to the official shall be presented at the scorer’s table where a coach of each team may be present.

10-5-1c. The head coach may stand and/or leave the coaching box to confer with
personnel at the scorer’s table to request a time-out as in 5-8-4.