There's several issues at stake here. The first is that these guys are under extreme amounts of stress. The level of stress the average soldier faces in a war zone (and that's what it is) is unimaginable to pretty much anyone that hasn't been there. I've heard stories of some things these guys are faced with, and none of it is pretty. I've had to take a step back from some of it, and I didn't even experience it directly. When you get an RPG shot at you that bounces off the front of your Humvee and by some miracle, it doesn't go off, you don't walk away from that the same. Having to stab someone repeatedly in order to save your own life. Shooting at actual people. Not some representation of people, but actual living, breathing human beings, and seeing the carnage wrought by your bullets. It's hard to even comprehend.
Now, imagine these guys come back and are generally able to continue to carry on some sort of a normal life at home. There's a lot of training involved here, and part of it is that you were simply ordered to do it. The chain of command is a real force, something the average soldier respects enough to go into a situation that very well could end their life. They also fear it. It's a force that's almost worse than death. Would you want to admit mistakes, or would you feel better about simply covering them up? This hypothetical soldier is already hardened enough to take the life of another person without feeling intense amounts of guilt. What is covering up a mistake compared to that?
There's also an insane amount of camaraderie amongst soldiers. These guys are willing to go into the line of fire to get back a piece of their buddy to send back home, because no soldier gets left behind. Would you risk your hide to get back part of your friend's dead body in order to have a proper burial? I don't know if I would, but that's a fairly ubiquitous feeling amongst soldiers. These guys will fight and die for their fellow soldiers, dead or alive. If you would already put your life on the line for someone, why wouldn't you help them cover something up?
Finally, the perception of people (civilians or combatants) from the view of a soldier is horribly skewed from what it is at home. They aren't really humans when they're on the battlefield. They're targets. The guilt doesn't really hit until after these guys get home. When you're in the midst of it, you're worried about your own survival, and the survival of those you care about. They don't seem to be particularly worried about the collateral damage. If they make a few mistakes, oh well. It's better than not pulling the trigger and finding out they were actually the enemy.
I'm not saying it's okay. It's certainly deplorable behavior. I'm just saying it's understandable, from where I sit. If I were put in a similar situation, I'm not sure how I would react. No one does, but the only way to prevent is to simply not go to war.