Exactly, its not a very complicated case at all. There are any number of very simple ways to explain this.
Hypothetically and backup up by some evidence: They were both very drunk. He got out of the car and kneeled to get sick or fell into the street near the curb facing so the back of his head was toward the rear of the car. She backed up and hit him going 20ish miles an hour and dragged his arm through the wheel-well as she sped off in the forward direction. This caused the injuries to his head and arm. He stumbled away to die in the cold.
She returns home and wakes up still a little drunk but realizes something happened and re-traces her steps because she left him somewhere, but can't remember exactly where, and he hasn't responded to any calls or texts. As she drives she starts to connect the dots and realizes the most likely thing is that she hit him.