It can happen. Break a limb and sustain an internal injury in a fall. While the docs have all their attention focused on the limb, the untreated internal injury turns fatal.
Very, very true- learned this as a kid. My best friend, who was 13, was on his newspaper route (45 years ago), when the brakes on his 10 speed broke. He went head first into a tree. The doctors were concentrating on his brain- and only his brain- in the hospital. He died of a ruptured spleen.