I was discussing LNT with a couple of folks on a website, and they presented two common misunderstandings.
1. LNT is bad because it doesn't account for differences in background radiation
LNT deals with cohorts in a population. One cohort has been exposed to excess radiation, the other has not. We want to observe the EXCESS risk associated with the EXCESS exposure. There are plenty of factors that make different populations have different background cancer rates. One is the background radioactivity. But there is also the underlying gene pool, diet, air pollution, etc.
By focusing on the excess radiation risk with a large enough exposed cohort, we assume that the other factors will cancel out between the two cohorts, and so background radiation isn't very important.
2. The statistical detection threshold of LNT could be an effect threshold. There might be some second order biological phenomena occurring.
Provide it. There is no evidence of it, and just because one can imagine one, doesn't mean it exists. The imagined second order biological phenomena might also increase the risk below the statistical detection threshold, though it couldn't be very much or it would be statistically detectable.
We stick with the evidence at hand. With new evidence, we adjust our conclusions.