Although that's totally the common understanding, surprisingly there's rather a lot of evidence (https://en.wikipedia.org/wiki/Radiation_hormesis) at this point that it isn't actually true; it's just a little hard to say "a little radiation might be good for you" without people writing you off as some sort of crazy person at the outset, so it's not talked about very much.
What you're describing -- and what most people who don't have a specialized education in the nuclear field commonly believe -- is something called the "linear no threshold" hypothesis (https://en.wikipedia.org/wiki/Linear_no-threshold_model) of radiation exposure, and although it's commonly used because it's definitely the safest and most conservative way of responding to radiation exposure, it's rather controversial and probably wrong.
If you're curious and want to find out more, there's a lot of fascinating material about the subject available publicly, including some analyses of life expectancies in areas that have much-higher-than-normal background radiation (off the top of my head, Kerala, India is one such locality).
What you're describing -- and what most people who don't have a specialized education in the nuclear field commonly believe -- is something called the "linear no threshold" hypothesis (https://en.wikipedia.org/wiki/Linear_no-threshold_model) of radiation exposure, and although it's commonly used because it's definitely the safest and most conservative way of responding to radiation exposure, it's rather controversial and probably wrong.
If you're curious and want to find out more, there's a lot of fascinating material about the subject available publicly, including some analyses of life expectancies in areas that have much-higher-than-normal background radiation (off the top of my head, Kerala, India is one such locality).