Their "worst case scenario" involves running 365 simulations based on daily weather patterns and adding up the dead.
It also assumes an attack launched by a super-power capable of delivering 450, HUGE nuclear warheads and every one of them hitting their target. And, I assume, they assume the fallout will include the plutonium in the warheads in the silos that the incoming weapons are supposed to vaporize.
This post was written in 2013 by Alex Wellerstein and I think it contains a lot of useful information. In my humble opinion, it is not "Fear Pron".
Key points:
...terrorist nuclear weapon manages to combine the worst aspects of both: targeting civilians and kicking up a lot of fallout, for lack of a better delivery vehicle. ERJ adds: and have low fission yields so much of the plutonium is not consumed
...fallout mitigation is one of those areas were Civil Defense is worth paying attention to. You can’t avoid all contamination by staying in a fallout shelter for a few days, but you can avoid the worst, most acute aspects of it.
Weapons that are designed to flatten cities, perhaps surprisingly, don’t really pose as much of a long-term fallout hazard. The reason for this is that the ideal burst height for such a weapon is usually set to maximize the 10 psi pressure radius, and that is always fairly high above the ground. (The maximum radius for a pressure wave is not intuitive because it relies on how the wave will be reflected on the ground. So it doesn’t produce a straightforward curve.) Bad for the people in the cities themselves, to be sure, but not such a problem for those downwind.
Personally, I think we will see terrorists-type nuclear attacks before we will see broadside exchanges. Any nation-state competent enough to pull off the broadside is smart enough to weaken us by using a proxy. Sort of like those tiny spears the clowns jam into the bull's shoulders to make it lower its head before the matador enters the ring.

