I think mutation rate would be subject to evolution as well. We can evolve to do more, or less DNA repair (and checks; up to acute radiation poisoning, cell self destruct is good enough).

Also, the effects of radioactivity are presumed linear. Extrapolating from high doses, the doses of up to 10x our natural background must have extremely minor effect on the mutation rate, vast majority of mutations arising due to other causes.

(The radiation releases in nuclear accidents are only a big deal because very huge number of people is exposed, resulting in massive dis-utility even if cancer rate increase is very minor)