I think there is a disconnect in meanings of trigger-happy. Yours seems to be what people familiar with guns mean, and the other was colloquial “too willing to use a gun.” So you disputed both meanings, but you’re not going to persuade the other side by saying he was actually very trained and skillful in what they see as an unjustified killing. (Not really taking a side personally as I haven’t watched or read much about the death.)
Having watched the videos now, he appears to shoot 2 rounds through the drivers window, after whatever amount of personal danger he was in while in front. That seems closer to mag dumping and poor discipline than not.