Some of Andrew Sullivan's readers do a nice job taking apart the pernicious "there's no looting in Japan" myth by citing stories of, well, looting in Japan. So while one angle here is that Japanese looting has been underreported, the other is that American looting has probably been overreported. The media reported many stories about looting and other illegal behavior in the days after Katrina made landfall in Louisiana. However, as Cooper and Block noted in their book Disaster, these stories were often false or grossly exaggerated. Moreover, they point out, these reports tended to ignore another notable human reaction to the collapse of infrastructure: spontaneous community building. The book cites numerous instances of people banding together to create kitchens, shelters, and modes of transportation in New Orleans at a time when local, state, and federal governments failed to do that.
Japan's a big country. No doubt some people are looting, while others are trying to help each other, and others are just trying to stay alive. You can report on whichever aspect of this you want, although the resulting story is probably more reflective of the culture of the reporter than that of the afflicted country.