We know the mechanism by which radiation causes damage: Particles knock into DNA, changing its structure. This causes mutations, and once too many of those accumulate, you get cancer, or your cells just stop working and you die.
This would suggest that the risk should be linear with radiation dose. But cells have DNA repair mechanisms. If a person receives a very large dose in a short amount of time, it makes sense that the repair systems might be too overwhelmed to fix all the damage that has occurred. Of course, the repair system isn't perfect, and some small fraction of damage will be permanent. This suggests that LNT should be true for small doses, but the harmfulness of radiation per particle should increase at larger doses.
A few consequences if that's true:
Depending on how the constant coefficient is determined, a fully linear health risk model will tend to overestimate risk at low dose rates, but underestimate at high dose rates.
This also suggests that radiation concentrated in a particular spot on the body is particularly dangerous. The cells in that location will be bearing the brunt of the radiation dose, so their repair systems are more likely to fail. So inhaling a bit of plutonium dust means you're in for a worse time than absorbing an equivalent dose spread out over your body.
Of course, whatever health risk model we choose, it should also be applied to the regulation of coal plants, since they put radioactive isotopes into the atmosphere as a part of their regular operation.