Most (if not all) nuclear scientists and radiation experts I've seen tslking about this say this is a wrong assumption. Cheryl Rofer, former nuclear scientist, made a napkin calculation and suggested it would need about 57 years of camping in the hottest (= most irradiated) parts of the red forest to acquire ARS (acute radiation syndrome). Even if the digging and kicking up dust there elevated the radioactivity levels, it would take a hell of a lot to get from 57 years to one month. Keep in mind that the most radioactive snd thus dangerous elements also decay the quickest, because of course both properties stem from the same thing, redioactive decay. The more dangerous the quicker it's gone.