Katrina represented a failure of government at all levels even before the hurricane made landfall. Aging levees failed, pumping stations that were supposed to keep sections of the city dry were not maintained, etc. It was very much a failure of the city's infrastructure.
It appears that Houston was not a "failure of infrastructure" at all. The city was simply overwhelmed with a volume of rainfall that exceeded the design standards used for any storm water management system.
Though the initiating causes were different (on that point you are correct), the solution was the same. And that solution wasn't initiated or even driven by government, but by people's individual decisions.
Each individual owner of boat/motor/trailer/tow vehicle made the decision to give freely of his time, and risk his material goods and even his life in the service of his neighbors.
And Bray is correct....those individual decisions ultimately had their roots in Christianity, even though in many cases the deciding individual might not have even been Christian.