"it is as much a matter of winning hearts and minds as it is taking out the enemy - only this will bring long term peace and trust"

Precisely. America's relationship with Pakistan was already damaged enough prior to this incident, I can't see that publicly humiliating the Pakistani government and people will help to repair that damage. As for the so-called 'war on terror', as others have said, only time will tell as to whether this will be shown to be a strategic faux pass as well as a diplomatic one.