The reason is that your body has mechanisms to fix the problems of radiation. For example, when you drop a stone in water would you say that you "break the surface of the water"?

Our DNA is very similar - DNA damage occurs naturally. Our body has processes that fix DNA strand breaks. Radiation that occurs because of most exposure that has ever occurred is so minimal that the body's natural defences against radiation damange means that the harm is precisely zero. The body literally repaired itself much like that water surface repairs itself.

Harm does occur however when the rate of radiation exposure exceeds our body's ability to repair itself. However this threshold is well above any threshold we regulate around.

For more information the key words are "dna double strand breaks" and "LNT vs SNT"

I read it thusly: not "(mostly precisely) zero" but "mostly (precisely zero)"

i.e in most reasonable cases the risk is exactly zero and conversely it takes extreme scenarios for the risk to be non-zero.