As far as American law goes, you are very wrong with regards to when deadly force may be used. Generally, it's okay to respond with force that is likely to cause death or serious injury when the same is imminent to/upon a person being attacked, or when one of several forcible felonies are being committed upon a person (murder, rape, sexual assault/battery, arson, treason, car-jacking, robbery, planting bombs, etc.). Vigilantism this is not, as the use of force is explicitly authorized by the law.

I guess we Americans place a lower value on the lives those who initiate violence.