It's been a long time since law school, but I'll give this a whirl.
Insurance policies such as homeowner's policies, umbrella policies and probably the NRA policy insure you against actions arising from your negligence or strict liability (applies mostly to real property, such as when a tree falls on someone's car in some states.) I know of NO insurance policies which cover intentional torts (that is acts which give rise to injury in another person-tort, which are done on purpose-intentional.) There is also a point where reckless disregard for consequences can free the insurer from its obligation because reckless disregard is not negligence.
So, if you intentionally pull the trigger on someone, you're not going to be covered. If you accidentally discharge a weapon and hit someone, you MIGHT be covered if your actions are not so reckless that you aren't covered.
More bad news: intentional torts usually open the door to punitive damages, and awards based on intentional torts usually cannot be discharged in bankruptcy proceedings, IIRC.
Just goes to show you better really need to when you pull that trigger, because you may be putting all your worldly goods on the line.
By the way, LEO's usually have immunity or indiemnification as long as they act within course and scope of duty.
Hope this helps.