I'm going to undo a bunch of mod points with this post, but I wanted to point out that the blog post you cite is flat out wrong.
I'd like to say that I'm for building more nuclear plants of 4th or later generation design and that even with the LNT model, the maximum number of deaths from Fukushima might be on the level of a single bus accident. That said, the blogpost is incredibly misleading. It took me a while to track down the original source that the post claims to cite from UNSCEAR and it's this paragraph:
In general, increases in the incidence of health effects in populations
cannot be attributed reliably to chronic exposure to radiation at levels that are
typical of the global average background levels of radiation. This is because of the
uncertainties associated with the assessment of risks at low doses, the current
absence of radiation-specific biomarkers for health effects and the insufficient
statistical power of epidemiological studies. Therefore, the Scientific Committee
does not recommend multiplying very low doses by large numbers of individuals to
estimate numbers of radiation-induced health effects within a population exposed to
incremental doses at levels equivalent to or lower than natural background levels;
What they are saying in short is that the statistical uncertainty is strong enough at low levels of radiation doses WRT cancer risk is that it's not possible to tell whether the LNT model is true or not and THEREFOR it shouldn't be used to say "this many people will die from this much low level radiation". They aren't saying that LNT is wrong. They aren't saying that LNT is right. They are saying we don't know.
The quote from the report is from here. It's from the latest report to the general assembly, page 16.