Why should they make any assumptions? If no 'statistical' increment can be detected, and "statistics" is still science, then doesn't this resolve the matter?
No, it doesn't resolve the matter, since the lower bound on detectability is still a very large number of cancers (most of which will not have occurred yet).
Understand that regulation is not like criminal law. Radiation does not have to be presumed innocent until proven guilty.
That's such a strange thing to say; no-one is suggesting that radiation gets a presumption of innocence. As far as I understand it, there's no generally agreed viewpoint on the expected effect size for exposure to low levels of radiation. In this case, there was discovered to be no statistically meaningful effect. This is now something that new that we know.
The question becomes: how should low doses of radiation be regulated?
One approach would be unless you can prove the radiation is having an effect, it gets a free pass. This would likely result in substantially larger population exposures. If enough individual sources are given free passes, eventually the dose accumulates to something that would have an obviously visible effect.
Another approach would be precautionary: assume radiation has the maximum effect not ruled out by evidence. This would result in much stricter control than current regulation, which assumes the effect is linear down to zero dose. Some anti-nuclear activists have objected to LNT because they think it's underestimating the effect of radiation (not that they have good evidence for that.)
Current regulation is between these, assuming linear effect. This is a biologically reasonable assumption, since at low doses the number of affected cells is proportional to dose, and it's unlikely any single cell is directly affected more than once. It also takes into account the cumulative, additive effect of radiation exposures from multiple sources.
That's not the way statistics work. You won't be able to definitively state there was an increase in the number of cancers based on statistics if the actual increase was smaller than the uncertainty in the number of cancers you would expect. That doesn't mean the increase was zero.
Except it's not "we really don't know", it's "after looking at thousands upon thousands of cases over many decades, there do not appear to be any statistically relevant effects".
But that's not how that works? If there is no statistically significant effect, then whatever effect there might be is so small that it's part of the background noise: we have a complete enough answer to say "there is nothing that can be attributed to just this thing". And we can say that with certainty because of the statistics.
From this specific accident. However, the evidence from radiation biology in general is that there should be a certain number of cancers (and no, don't feed me anti-LNT BS.)
But, you know, probably fewer than accounted for natural variations in the background level caused by different rock types in the area or exposure to residual fly ash from thermal power plants, right?
It seems fairly obvious that if the influence of a nuclear accident on cancer rates is dominated by other factors, one should look to mitigate those other factors before worrying about the nuclear accident as a contributor.
Understand that regulation is not like criminal law. Radiation does not have to be presumed innocent until proven guilty.