Natural Born Killers opens with Mickey and Mallory's largely unprovoked murder of five people in a diner. From there it travels back in time to show how Mickey met Mallory, went to jail briefly and escaped, came back to get Mallory and help her kill her parents, and married themselves standing atop a bridge. The movie then skips ahead to after Mickey and Mallory were captured, showing clips from the tabloid news show "American Maniacs," featuring interviews with Mickey and Mallory's fans and reenactments of some of their crimes. The events in this part of the film are clearly identifiable as being from the media's perspective, but it quickly switches back to its initial narrative perspective to fill in the events that lead to Mickey and Mallory's capture, all the while portraying them in the same, rather positive manner. The only other part of the film that is clearly from the media's perspective is a short montage about Mickey and Mallory's trial right before the film's climax, the prison break.
The fact that the film begins near the end of Mickey and Mallory's murder spree and then goes back to explain how they got to this point serves to further excuse their actions. Going so quickly back to Mallory's life in an abusive home indicates that the home was responsible for that circumstance in which we initially saw her. So through this decision about chronology, Stone has further muddied his argument by making Mallory even more sympathetic a character, and Mickey more heroic for rescuing her from this situation.
Had the "American Maniacs" clips introduced and concluded the film, everything portrayed within the film could have been claimed to be from the media's perspective, thus both making Stone's argument clearer and also making Stone much less responsible for misinterpretations of the film. Perhaps Stone intended for the whole film to indeed be seen as portraying the killers the way the media does, but this simple switch in chronology could have easily solved the problem.