The humans are not the source of the radiation that made it sick, it's the radioactive materials. Have a look at what typical urban environment radiation levels are, they are about 4x as high as the ambient in the external areas (not near metal objects) in Pripyat. There is a lot of radioactive material that is permitted by governments to be in many things, the most notable being phosphate fertilisers, where there is a mingling of the mineral source with a fluoride-containing mineral that also usually contains trace uranium.
What's more remarkable is that, although the efforts to encapsulate the reactor were quite heroic and they shut it down in 6 months, even still, with the Red Forest completely dying, in merely 30 years it has come back. So the gloom and doom about nuclear disaster is quite overblown. Most people don't even realise that nuclear weapons, especially the newer ones, barely leave any radionucleides behind, they explode very efficiently. The same cannot be said about depleted uranium used in small munitions however.