If anything, FEMA tends to grossly underestimate the impact of the incidents they may respond to; the public tends to grossly overestimate FEMA's capacity and interests in doing what is ultimately, for every animal and man since the dawn of time, their own job and no one else's.
I think that's a bit harsh. Civilization gives us infrastructure to live safely in very densely populated areas. When that infrastructure fails it doesn't seem fair to just say: "Now it's up to you like it was up to your ancestors. It doesn't matter that they didn't live in a spot where they had 100k other homo sapience specimens within half an hour walk, now competing for resources that stopped flowing in."
It's so insanely densely populated that even leaving this place in a car could take you days.
Civilization allowing you to live without regular incidents is different from it allowing you to live safely. The marks of civilization (namely density) become liabilities when things go very wrong. In many ways, it's up to you in ways your ancestors never had to deal with: more things in civilization burn, crush, lacerate, and impale people when they fail than in nature, and nature had plenty of these to begin with.
A sense of safety built on the responsibilities of others is false, I think. Ideally we all do our jobs when the going gets tough, but in reality, you're surrounded by cowards who would rather watch you and yours die than put themselves in danger (see the recent mass shooting, where four deputies basically just stood outside for the duration of the attack), and in some sense, who could blame them?
I don't know how much canned chili you keep, but FEMA recommends keeping at least a 3 day supply of non-perishable food on hand. I don't think FEMA has a reputation for having borderline paranoia.