It's not about being trigger-happy, it's the focus of thinking.
The military's job is to defeat enemies. If you are a soldier, enemies are people who want to kill you, the soldier. They're enemies when everyone wakes up and they're enemies when everyone goes to bed. So the soldiers' job in-country is to sort people into enemies and civilians; to defend civilians and kill enemies.
In the U.S., a police officer's job is to enforce the law. They are supposed to be policing behavior, not sorting people. Everyone is a civilian. A civilian who broke the law is not an enemy, and the justice system is not seeking to defeat them. The law is supposed to punish behavior in proportion to the crime, and in accordance with the written law.
Now of course it's not that simple; there are organized crime syndicates, like drug gangs or terrorist cells, who target police. But the reality is that those are a tiny tiny percentage of the population.
But law enforcement has spent a decade re-organizing itself to defeat them. That's how you get an "Emergency Response Team" (SWAT) setting up a secure perimeter and clearing houses around a sleepy veteran who just called for a little support, as in this story.
They didn't show up to help a veteran; they showed up to defeat an enemy.