Art, I believe you are correct. I believe I have run across stats showing declining capital crimes.

I don't think most people in America need to worry much about violent crimes or rioting due to natural disasters for the first few days post event. Shock, fear, disruption, hope, stocked resources all lead to a sense that the system will right itself quickly. As the timeline expands I think people will become progressively more protective or aggressive.

This is not to dismiss the emotional reaction to human responses that cause wide spread damage like LA/Watts/Chicago riots, Anarchists, etc., which spark immediate aggressive mentality though usually contained to a specific area, as you mentioned.