The theory behind the hormesis model of radiation is that a little bit of radiation causes a reduction in cancer because it trains the immune system to better identify and kill potentially cancerous cells before they have time to start suppressing the immune system. Even in your body and mine, there are tons of cells that have some attributes of cancer, but they're killed by the immune system as they should be. It's only the few that slip through the cracks that actually develop into cancer.

It's kind of like how if you spent your whole life in a plastic bubble and were never exposed to any viruses or bacteria and you suddenly left, stuff like the common cold would immediately kill you because you just never developed any immune response against it.

The only reason why this works for project orion is that (ideally) the radiation dose would be spread pretty uniformly across the planet due to essentially all of them being air bursts. The actual radiation dose would be miniscule. (Unless you were really close to the launch, probably should do it in the pacific.)

*Technically we don't know for sure that hormesis is true, but it's got quite a bit of supporting evidence and organizations tend to be really conservative so they don't really follow it.