The answer espoused herein is speculative; but I find it so plausible, I'm going to declare it to be settled science, which oxymoron means you are not allowed to shoot it down. The piece requires a little background in radiation, including the definition of a gray(Gy). It's just the amount of radiation energy in joules deposited in a kg of tissue.
Natural background radiation on most of the planet is less than 3 mGy per year. There are a few areas where background rates are up to ten times this level, and a few tiny, highly localized spots still higher. But it takes protracted dose rates of about 20 mGy per day to produce detectable harm in a human. The obvious question is: why would nature equip us to handle dose rates that we probably never encountered in the evolution of the species?
The standard answer is our DNA repair systems are there to protect us against all the damage caused by our oxygen based metabolism, which is far worse than the radiation damage. The DNA in our bodies is constantly being assaulted by Reactive Oxygen Species(ROS). These chemical active molecules such as OH- are the by product of oxygen based metabolism. About one-billion ROS micro-bombs per day per cell leak from our cell's mitochondria into the rest of the cell. Roughly 1 in 20 thousand of these molecules chemically damage our DNA.
To over-simplify slightly, Double Strand Breaks (DSB's) of the DNA helix are the form of damage that leads to cancer, since error-free repair cannot be guaranteed. Radiation can also cause DSB's. But it would take 250 mGy/d of radiation to produce the same number of DSB's per day as created by our normal metabolism. Therefore, it is hardly surprising that any harm associated with 1 mGy/day is undetectable. But once we are dealing with dose rates of 20 mGy/d or more we start to see harm. At that point the cell is dealing with significantly more DSB's than normal.
Figure 1. Endogenous DNA damage to O2 metabolism is equivalent to 250 mGy/day radiation.
OK, but this begs the question: how did oxygen based metabolism get started? Could O2 based metabolism have developed without a pre-existing DNA repair system? The answer is almost certainly no.
Cyanobacteria were around for about two billion years before oxygen breathing organisms developed. These algae can convert sunlight directly to life-sustaining chemical energy. In the process, they produced the free oxygen which allowed O2 breathers to develop. Floating on the surface of oceans and lakes, they were exposed to many times current ionizing radiation rates. At the time, there was no ozone in the atmosphere to shield them from high intensity UV-C photons.
Some of these organisms became very good at repairing radiation damage. Sandia studied three that were almost as radioresistant as D. radiodurans, Figure 2, the all time champion in this contest (so far).\cite{jensen-2016}
Figure 2. Percent survival after exposure to Co-60 photons at > 1.5 Gy/s. The numbered bugs are cyanobacteria.
These three were desert dwellers, who go dormant during dry periods. They probably developed this ability in order to quickly repair the damage that accumulated during dehydration. Billi et al studied one desert loving algae and came to the conclusion it could survive a 15,000 Gy dose, delivered over a period of days. They comment
The severe DNA damage evident after exposure to 2500 Gy was repaired within 3 hours, and the severe DNA damage evident after exposure to 5000 Gy was repaired within 24 hours.\cite{billi-2000}
But even normal cyanobacteria are pretty good at repairing radiation damage. Badri et al studied an edible algae called Arthospira, and found that it could survive 6400 grays delivered at a dose rate of 527 Gy/h.\cite{badri-2015} Arthospira is high in protein, and shows up in some health foods, under the name spirulina. NASA wants to grow it on space ships. At the molecular level, the enzymes that were upregulated by radiation were different from but similar to the ones we use.
Like us cyanobacteria are mostly water. The main mechanism for DNA damage was:
1) photon energy ionized cell water,
2) the resulting ROS chemically reacted with and modified DNA.
Cyanobacteria had well developed ROS repair systems long before any oxygen metabolizers were around. Our eukaryotic ancestors incorporated bits of cyanobacteria into their more complicated cells, and co-opted those systems. They then improved on them to handle the even larger ROS production rates associated with oxygen metabolism.
In short, the reason we are so good at handling radiation is we must be able to repair DNA damage from O2 metabolism; and the reason we have O2 metabolism is Archean algae had to be very good at repairing DNA damage from radiation. We stole and built on that system. That's my story and you will stick to it.
Food can be sterilized in its packaging using ionizing radiation. Exposures are limited to 1000 Gy, I think. I wondered where the food-borne bugs would fit on your Figure 2.
https://en.wikipedia.org/wiki/Food_irradiation
https://www.cdc.gov/foodsafety/communication/food-irradiation.html
Interesting theory, sounds plausible and definitely more plausible than the radiation models that have been used to justify killing off nuclear power. A chart with memorable quantities contrasted with each other would be useful here. Something like low to normal, a threshold where damage becomes significant compared to the background damage from oxidative processes, and some examples of large dose events (6 hour flight, Chernobyl core containment crew for a day, Manhattan project criticality accidents, visiting Kerala for a week).