There is a wide berth between "thinking twice", hestitation and "shooting first, asking questions later."
If this detective shot this suspect, and the shooting was caught on film, would it have led to all sorts of internet outrage and memes...? Probably.
If the dectective said "I was scared he would overpower and take my weapon, then beat me with it", would the responses would have been rolling eyes and talk about how an unarmed man cannot be dangerous...? Probably.
On the other hand, police are not only paid to make the hard decision, but also to explain it.
For a very harsh example of fatal hestitation, refer to:
https://www.youtube.com/watch?v=k8-ycSkoYfc