I wasn't there, so I dont know, but I find it very hard to believe that special forces who just fought their way in to the enemy's holy grail, and who may very well have to fight their way back out to safety, are going to waste time, energy, and ammunition mutilating a dead body. Every round wasted on a dead body is a round you can't use to try and kill the next live body that's still gunning for you.
Maybe I'm wrong, maybe it did happen this way, but it'll take a lot more hard evidence to convince me.
I agree with your points in general. These are Tier 1 operators, and emotion (Anger, especially) causes mistakes. That, however does not necessarily make them immune-- especially with this target.