Why would you worry more about tungsten rods? 1) They're incredibly expensive because tungsten isn't exactly common. 2) You fire them and they don't explode, they penetrate. They're bunker-busters, meant to get into hard targets with high precision. Nukes are a little less discriminating.

Consider a WWI analogy. Would you worry more about a machine gun or mustard gas? Both can kill you, but you worry more about the mustard gas because if the wind changes, you're the one breathing it right along with your enemies.

There's a reason nukes are heavily regulated under international treaties and tungsten (and similar armor-piercing tech) are considered conventional weapons.

As for the conspiracy theory about Hiroshima, how would you explain the cancer rates? Firebombing doesn't cause cancer, but radiation does.