I think the key to remember in any such confrontation is whose interests are really at stake.
In this case you (seemingly) have a templar pissing flames because their
personal plans got messed up. The Templarate seems to have gotten its own. The sarge says he apologized and returned the money. Templarate is probably fine with that. Compare that with the Byn being asked to hand over their own for what seems like a dubious execution. If they go along with that, it creates long term problems for the organization, not for Copper personally.
So, the Lt is fighting on behalf of an organization against an individual Templar. That works. If this was just an argument between Copper personally and the templar, taking the tack that she is probably would not have ended as well.
Another thing to remember is that if a commoner bucks the system (refuses to show at least a base level of respect to a templar/noble) they represent a threat not just to that noble's pride, but to the
feudal foundation of the entire city-state. That's more trouble than most people can handle. Copper is firm, and speaks her piece, but she still at least addresses the templar by his title, and when she wants to say "no" she says "no". She
doesn't tell him to "pound sand". Important note there for any would-be ballsy types.

Courageous confidence needs to look different than suicidal stupidity!