No one here was there & knows the situation with the kid, maybe he needed more than conventional punishment but I think we all can agree taking the family sedan w/o permission is not a death sentence crime. But anytime you are confronted with arrest, you could be killed.
I knew a kid who lived down the street from me when I was a teen who was a little rough around the edges, he was throwing a fit & his parents, who were fairly old to have a teenage son, called the police & told them he was tearing the place up & they couldn't control him. Well, when the cops got there they ordered him to come outside over a loudspeaker & he did. When he came out, he was holding a piece of water pipe he was wrecking the place with & a local detective named Pokey Gibson mistook the water pipe (he claims) for a gun & gutted the boy with a 12 gauge shotgun. He died right there on the porch.
I don't have the answers, but I would never call the police on my kids. If I couldn't handle them i suppose I would get help from some friends & evict them from the house. I just don't know; I am thankful I am not faced with such dilemmas.