My guess is the law dates back to pioneering days or something.
The article shows how people who are basically criminals could obtain a badge by just knowing somebody. From the rest of the article, it seems like Greenhouse was previously threatened by Chris Few (the father in the car who was injured) after Greenhouse sent a message on Facebook to Few's on-and-off girlfriend and then visited her house. Don't know what that was about but you can make a couple guesses. Apparently on the night of the shooting, they weren't a couple and they had an argument in a bar parking lot after which somebody called 911.
That might explain the traffic stop and not having a warrant but then why would they come out shooting at a car that was cornered and with the driver having his hands up? At best, it's because they panicked.
I know there's got to be more fucked up details waiting to come out.