The Commander in Chief is however, despite your protestation, responsible for and in total command of the actions of the US Military and as such determines the rules by which they will engage the enemy, which he sends to contest.
As such, it is the CinC which retains the final authority for all matters regarding the US Military, which decidedly includes the rules of engagement by which the US Military operates. PERIOD!
I hope you don't mind bashing General McChrystal when you talk of "mamby pamby, psycho-absudities of trying to win the hearts and minds of the enemy" because that is his strategy, and even that phrasing of "win the hearts and minds of the enemy" is his.
Nope... 'Hearts and Minds' is a force multiplying tenet of guerilla warfare which goes back to Sun Tsu. The phrase "Winning the hearts and minds of the Local Indigenous People" is rooted in the mamby pamby bowels of the Johnson Administration and one General Westmoreland; Commanding General of US Forces in South East Asia. Circa 1964-ish.
Of course, Hearts and Minds only works when the player seeking to win the hearts and mind are sincere and virtuous. LBJ was not, Hussein is not and no Progressive is capable of such; thus the reason for Chronic Progressive failure in such matters; they're inherently corrupt; and the people attached to those hearts and minds, not being FOOLS, soon recognize that they're being played and turn to the highly dedicated, sincere INSURGENCY!
Nothing particularly complex about this... It's human nature and there's no mystery left in such matters.