No more than officials are supposed to accept whatever a coach says, no matter how wrong they may be. And they can be wrong.
Oh, they can be quite wrong about the rules, quite often. I find it embarrassing to hear how wrong coaches can be. Unfortunately for officials, yes, you pretty much have to listen to what they say, within reason. You don't have to agree with it, you don't have to rule in their favor, but if they do it it properly, you have to listen. Comes with the job.
Last year, an entire coaching staff - all 7 of them - insisted a crew gave the opponent 5 downs in a series. After reviewing the film, including down, distance and a copy of the play-by-play, we found the "extra" down came because - cue the band - they thought OPI still carries a LOD. Really?
Wrong, but not outrageous. They just weren't up to date. But you couldn't straighten that one out?
And believe me, they were closer to "up to date" than the H who this past season told me Illegal Procedure certainly was a penalty in HS football, and he pulled out his signal card to prove it to me. Sure enough, his card said signal 19 was Illegal Procedure. I think it also said Lyndon Johnson was President, but he didn't let that get in the way of his ignorance.
I guess the crew could have reported the coaching staff to the state and kept them from coaching in the playoffs.
If you think that will get you anything other than laughed out of the office, then have at it.
Look, coaches make tons of mistakes, I'm not defending them. And if they were to do something egregious (shoving an official, or an opposing player, or instructing his players to intentionally injure an opponent, etc,), then they absolutely should be reported to the state and banned from coaching in the playoffs. But if an officiating crew completely ignores or misinterprets a rule, and refuses to look it up or allow it to be looked up, then they too should be reported and removed, as they obviously aren't competent to do the job at that level.
Your crew won your battle; you won your war (your words), and the crew suffered consequences. Too bad those battles and wars are only fought on one front.
But they aren't. There are a number of coaches around our state that served suspensions last year because the officiating crew filed a report. Far more than the other way around. And I'm betting most all of them deserved it.