What you say about your husband doing tasks even when injured, that is normal for soldiers, as we're taught to fight through the pain and keep going. You don't lose it.
Agree to disagree, sure... though please be aware I am up to date on the psychology behind military training, and I suspect your husband knows it more than he may think specifically about the psychology, but would recognise the below statements made.
but it is intended to overcome the "flight" side of the flight/fight response
You can't say that military training is intended to overcome the flight side of the response (singular). Training is designed to actually overcome the freeze response, that is combat trainings primary objective. They don't want you to freeze, because freeze is dangerous.
What training achieves is it teaches the ability to fight / flight with accuracy. When to fight, when to flight. Flight is actually taught as part of tactics, and is not just a withdrawal component, but flight is enhanced when taught, teaching tactics of when to flight from x and fight from y position instead. Flight / Fight go hand in hand in tactical combat, we soldiers ARE NOT taught to override it at all. That is completely incorrect based on the fundamental psychology of tactical combat training.
It's like changing to a flanking attack, were fighting forward may not be allowing you to advance as fast as you need or as safely, so the commander of the team will send x members into flight (withdrawal) whilst others provide covering fire. Those members then tactically pursue a different agenda to enter the Fight again.
Combat soldiers ARE NOT taught to override flight as a singular premise, only freeze (and only freeze in a combat fire situation). So sure, agree to disagree, but the theoretical writings disagree with your conclusion. Let your husband read this, he would understand the tactical logic in the underlying psychology of his training to confirm that it is only freeze trained out of us.
Freeze is attempted to be over-riden through repetitious drill training, fire and movement. Shot rings out, there is a repetitious procedure drummed into our head to follow and deviate as needed based on the situational assessment. A literal choice is made in the initial assessment to fight or flight, and this assessment is constantly being made by the commander at the time based on the situation.
I mentioned freeze in a combat situation, because freeze is also taught and enhanced (husband again) for when setting up an ambush. Soldiers lay still for hours on end, no movement, no noise, total freeze, awaiting the enemy.
In the sense of fight / flight / freeze when under fire though, that is where freeze is trained out of us as much as possible. Some still succumb to freeze, its a powerful response... but that is the only one taught to override and go towards / away from the danger, as freeze is deadly, fight and flight improve the chances to live another day depending on the situation. The usual ratio is 3:1 when engaged. More than that, most Australian soldiers will flight, because the odds become enormously stacked against you, though again, situational assessment determines the end action, as sometimes you must fight when outnumbered because flight may cause more casualties as a result of the landscape and exit.
Don't think of flight as running away when talking about soldiers, because that is far from what happens. Flight is used to tactically withdraw, which means a combination of fight / flight is being used to suppress whilst x soldiers fall back, then they suppress, repeat cycle. Flight is as much of a life saver as fight, to soldiers.