You are exactly right and they are trained to shoot to kill if they are going to shoot at all.
Sorry.
Wrong.
They are trained to shoot to
STOP.
There is a major difference.....shoot to stop means always shooting for the visible centre mass.......which on a man facing you is the centre of the chest......because that is the method that is most apt to stop the opponent continuing the actions that caused you to open fire. Whether he dies or not is immaterial.
That includes, BTW, head shots if two body shots prove ineffective.......known as the "body armour drill" Head shots are NOT prefered, because the typical male human head from the front angle has so much bone (insert joke here) that handgun bullets are routinely deflected or stopped. You are LESS apt to stop an assailant with a front on head shot that with a centre chest hit.
IF the cop said "shoot to kill" on a radio show he is an idiot, and did not understand the most basic part of his firearms training. In his defence, usually you say "shoot to stop" and the uninitiated HEAR "shoot to kill"
I used to teach this stuff, I know what I am talking about.