On the other hand, I disagree with this assertion:
if a microscopic piece of radioactive material gets into your body, you WILL get cancer -- may not happen for 10 or 20 years, but it will happen.
This is wrong, incorrect, unproven, and unsupportable!!!! Charcoal has minute amounts of radioactive isotopes in it, and you can lick it like a lollipop and you won't get cancer.
Radium or tritium coated watch dials are indeed radioactive and glowing like on the Simpsons...but you won't get cancer from eating a watch.
There's Americium radiating lotsa alpha particles in your smoke detector. It won't give you cancer.
Even standing in your clean house, you are bombarded by dangerous gamma rays, which cause cancer fer sure, but you may not get cancer in your lifetime.