There is a simple pill that would have prevented the difficulty. It is supplied in every nuclear emergency kit in Russia and available in Denmark and Sweden. Unfortunately it is not sold in North America.
Fortunately, however, the pill is quite simple to make. Ahead of time, obtain a quantity of potassium iodide from your local drug store. Five dollars worth should be lots. When needed, take a regular glass and fill it a fourth or less full of water, and then slowly start pouring in the potassium iodide while thoroughly stirring the water.
Don't worry about how much you pour in. You cannot pour in too much. After a while you will notice that the chemical no longer dissolves in the water. It just lies there on the bottom. This means that the water is saturated. You can now stop pouring in the chemical. More will not help or hurt.
Next take an eyedropper, or a soaked piece of paper if you do not have an eyedropper, and drop four drops onto a little piece of bread for an adult. Or two drops for a child. If you get several times that amount it is not going to harm you (although in much larger amounts it is a poison).
Now take some butter or margarine and make a little ball out of the bread and pop it down. Tastes awful. Ugh. Take once a day for 100 days after the last bomb falls. This is good stuff and you should have it around for reasons other than defense in case of a nuclear war.
If you live anywhere within in a couple of hundred miles of a nuclear generating plant you might suddenly find yourself needing the stuff. The US department of Health rushed a supply of pills to Three Mile Island and they have a standard brochure all printed ready for distribution in case it or some similar site vents.
The department of defense also keeps a supply near the old Titan sites that are deteriorating and breaking down. [Author's update note: Once again those sites have been now decommissioned and no longer present a problem, but much greater concerns now arise from Terrorist Threat, and the U.S. Government is now stockpiling in many cities not only these pills but others for Bateriological and Chemical Threats]. Canadians have nothing. I'll take that back. They do have lots of nuclear plants and the distinct possibility of bombs exploding over their heads and on their soil.
The reason why the potassium iodide works is that the thyroid will absorb only so much iodine. After that, any iodine taken into the body is passed off by the kidneys. Since the body already has all the good stuff it wants it passes out the bad stuff. This is what we call thyroid blocking.
Do not try to use the tincture of iodine that you put onto cuts. Taken internally it will kill you. And you cannot eat enough iodized salt to do you any good. You would get salt poisoning long before you got sufficient iodine to do the job.