My first question would be what was the score and who was winning? 

Normally, the team that is winning and has the game is in hand (2-3+ scores or more - 8 pts is all you can get in the standings) is way less likely to get a timeout granted with only a minute left.
I actually tell the officials to not grant these timeouts as we don't want any conflicts between the coaches after the game because of the perception that one team is trying to run up the score on the other.
We have seen way more pissed off coaches because of a team running up the score than coaches pissed because we wouldn't give them a timeout because they were winning big.       
On the other hand, if you were behind we would normally grant that request for a timeout to show your boys you are fighting until the end. 

You being an Big 12 umpire for 11 years I am sure you understand game management.  Such as when a team is down 10 runs the strike zone might get a little bigger for the team that is winning when they are hitting?   
just an example I could think of off the top my head. 

And if you would like a place in the NFHS rulebook to see where an official does not have to grant a timeout it would be under Rule 9, Section 9, Article 5. 
It reads, "Neither team shall commit any act which, in the opinion of the referee, tends to make a travesty of the game" 

All good points.  I will say, I figured you were on Offense though.   D is a little different situation, unless someone was calling a timeout on defense to get the ball back (not saying you were) 
Usually we can tell what someone's intentions are, might mess that up every once in a while though erring on the side of caution.  I apologize as it sounds like that every once in a while might be what happened to you in this situation.