While you are correct, it would be a tough sell to make. The first thing that would be thrown back, is that police tend to deal directly with people who have violent tendencies, on a far more regular basis than the average armed citizen. Second, armed citizens have the option of turning a blind eye to bad things as they occur; the police generally do not have such a luxury (unless of course, it's one of their own up to the shenanigans, but that's for another forum).
On the other hand, police generally have far less fear of legal reprisal when it comes to letting the bullets fly, than does the average citizen. Accidentally kill an innocent by-stander while defending yourself, and you're in for a bad time. If an LEO does it, the odds are about 50/50 that he'll suffer very little direct consequence.