This site doesn't seem great - their methodology doesn't explain how they reach the conclusions they did. For example, does radioactive fallout scale linearly with bomb size? I have no idea! But given that most weapons are hydrogen-bombs now, that doesn't seem intuitively obvious that it does - the amount of radioactive material per warhead plateaus while yield goes up and up.
Which is to say, it seems big on the "panic and horror" and low on actual information. I have no idea how to follow whether their conclusions seem reasonable or not.
For low-altitude detonations much of the fallout comes from irradiated dirt. For example the Baker nuclear test was the first sub-surface nuke and resulted in heavy radioactive contamination of the test ships.
Which is to say, it seems big on the "panic and horror" and low on actual information. I have no idea how to follow whether their conclusions seem reasonable or not.