Neutrons are the unusual dose they would have taken. Neither X-rays nor gamma will be coming through very strong after 4km of air, broadly equivalent to a couple of meters of water, despite the facetious film-rug statement.
There's some more information about them here:
Five Men Agree To Stand Directly Under An Exploding Nuclear Bomb : Krulwich Wonders... : NPR
All but one were officers, and presumably reasonably well-informed by the standards of the day.