As a kid I never understood the ending
But now I think I have it. The key is that Amy and Carol look sort of alike. So the newspaper printed that Amy had been murdered, along with Amy's photo next to the story.
Carol was approaching Amy's flat (being invited for dinner) when Amy was hiding from John (Jack) and he grabbed Carol, maybe from behind, and did not see her face.
But the police show up and get physically sick at the bloody murder crime scene. So when does John (Jack) abduct Amy at all if the crime scene is cordoned off from that point on? At least we have to assume that much.
"'Extremely High Voltage.' Well, I don't need safety gloves, because I'm Homer Sim--" - Frank Grimes