To me, how I want to see empathy applied in a military context, is nothing to do with familiarity or chumminess, and everything to do with the idea that, if you are my commander and you order me to battle, to fight and to die, that you do so carrying the full weight of that responsibility, that you understand my life and my worth as a human being, and that you empathize with the gravity and danger of what you are asking me to undertake, and that you won't spend my life in vain.
That is the real root of empathy, in the military, for leaders to really truly understand the both mundane and yet impossible weight of what they are asking their soliders to do. If you cannot empathize with the human condition at that level, then you should not be fit for military leadership (naive of me, I know).