It's not implying that it's specific to Yubari.
It's implying that it doesn't have the crime stats that are usual in decaying cities of the rust-belt.
Comparing decaying cities of the rust-belt with an average small city in Japan wouldn't be fair. Comparing them with a decaying city on the other hand makes sense.
http://en.wikipedia.org/wiki/File:Japan_earthquake_store_she...
http://www.theatlantic.com/daily-dish/archive/2011/03/why-no...
FWIW the main reason there is less looting in Japan is because they have done a better job at eliminating poverty. Here's what happened before they had done so:
Obviously, there is going to be some looting. But, consider a previous natural disaster of approximate magnitude* which took place a few years previously on a coastal city in the US. Compare the response by the US government, the Americans there, and more broadly American society. The Japanese have something figured out that Americans have forgotten, or more probably never had.
(*Not really, Tohoku was considerably worse than Katrina in magnitude and scope.)
Oh, come on. In the countryside farmers put vegetables in unattended booths for people to grab and put a coin in a hole for payment. Nobody's stealing. Where else in the world do you see that ?
But hey, weighing your produce yourself at the supermarket is also a thing here, and it works fine as well. Sometimes I think it's just a part of society, no matter the cultural, ethnical or economical background people have - if you trust them to "do the right thing", most suddenly feel sort of honoured and obligated to behave the right way. If you put police everywhere and assume people to be criminal first, they will act accordingly (test their 'freedom' as soon as noone is looking). It probably doesn't work if it's just one farmer / supermarket doing it, but I think when it's a common part of society, it suddenly works.
Immediately following the earthquake, transportation problems stranded many workers in Tokyo and cut off supply lines for stores. Those two issues combined with panic buying to result in the scene above shortly after the earthquake.