There is disagreement in the medical community for failing to distinguish the difference between and a low acute dose (less than 100 mSv but dosage accrued in a short time period, such as a single day), vs. a low gradual dose (e.g., less than 100 mSv but accrued over the course of a year)
The difference is that the bodies repair and disposal methods are thought to the be able to handle low-dose rates more comparable to high-level background radiation, than the unnatural effect of intense dosage rates that arise from nuclear accidents or bombs.
This is why the report you reference is not the high-quality support for the LNT model that you think it is. That report takes it's LNT data primarily from the low-level bomb data as 100 mSv - but 100 mSv for a single incident is nothing at all like a gradual dose of 100 mSv over the course of a year because the body for no chance to self-repair for that much radiation from a single incident.
The authors of that study frequently say that they don't have evidence that LNT is not the correct model. Not that they have strong evidence to prove that LNT is the correct model. I think the report is an honest assessment of the facts that they have.
I'm also not suggesting 100 mSv per year at a constant rate is perfectly safe - we don't have enough data to conclude that - for some reason the relevant double-blind studies never get done.
Others have suggested the acute doses less the 10 mSv are in fact safe or more accurately do not supply convincing evident that it is harmful. But public policy certainly does not support that view.