The pills, as stated, are for protection after radiation exposure, specifically to protect the thyroid gland, the main utilizer of iodine within the body (to produce the hormone thyroxine), radioactive iodine thus gets concentrated there and starts fucking up the thyroid, taking non-radioactive iodine in a large quantity (we normally need very small quantities for normal thyroid function) out-competes with radioisotopes of iodine preventing it accumulating in the thyroid and causing damage.
Similar, in a way, to how they treat MeOH poisoning, as it is the toxic metabolites (formaldehyde and formic acid) that damage the optic nerve and cause blindness, said metabolites are formed by alcohol dehydrogenase, the same enzyme that the liver uses to metabolise EtOH to acetaldehyde, then aldehyde dehydrogenase metabolises it further to acetic acid. Treatment is to have the patient drink a fuckload of ethanol, get them pissed out of their skull, and probably give them a rotten bastard of a hangover in the process.
The EtOH, given in such large amounts, competes for aldehyde and alcohol dehydrogenases with CH3OH, and prevents it being metabolized and thus exerting toxicity, allowing it to be pissed away harmlessly. I believe they may do so again with ethylene glycol poisoning, as its the oxalate metabolite that damages the kidneys.
They do, nowadays have a specific antidote other than a mass quantity of booze for treating MeOH poisoning though.