This sounds very, very similiar to I Am Legend.
That's what I was thinking too.
But I prefer to believe the official story, since zombies caused by viruses/genetic modification/drugs are boring and generic, people turned into zombie-like monsters by radiation on the other hand seems to be fairly creative, and besides, it makes very little sense for humans to destroy themselves with nuclear weapons in order to save themselves from a different disaster, two or more nations brining mutual destruction to each other over political disagreements makes more sense.