The bit about lung cancer and cigarette smoking being more relevant to their cause of death is very likely true - they will likely have had more radiation exposure, never mind chemical, from smoking than from their entire nuclear careers.

Cigarettes produce leave polonium and lead 210 in your lungs - which, while "only" an alpha emitter, being already inside your body has plenty of opportunity to do damage. Smoking a pack a day is about the equivalent of having a CT scan every day, due to the cumulative buildup of radioactive gunk in your lungs.