Not all radiation is created equal, and the delivery mechanism is very important.

Breathing in material emitting an otherwise harmless amount of alpha particles (essentially a helium isotope particle stripped of electrons) is very harmful. Those ionizing particles get into lung tissues and since they’re charged and have a lot of mass they can do a lot of damage in a local area. Internal doses are orders of magnitude more harmful.

Radiation is generally safe, but there are types of radiation doses that are very harmful. It’s less about the radiation level and more about what kind, how it’s delivered, and over how long a time span.