I recall a thought experiment that illustrates how small a molecule is, it ran something like:
If you take a single drop of water and drop it in the oceans of the world, stir THOROUGHLY, and then extract a drop of water-- it would contain (about) 100 molecules from the original drop.
In other words, the ratio of molecules to a drop of water is 100 times denser than the ratio of drops to the worlds oceans.
Take that 'fact' and combine it with the acknowleged 'fact' that 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.
So, perhaps you need a teensy disclaimer on your assertion.
You get zapped by many sources, like granite, radon (especially if you have a well - don't take long showers!), the sun, cosmic rays (much more so if you are a frequent flyer), your smoke detectors, etc.
Your body is adapted to some levels and types of radiation. Unless you exceed the human body's natural defenses against ionizing radiation, your chances of getting cancer do not go up.
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.