The study's conclusions I believe are flawed. That is, to say in a blanket statement that urban areas are safer compared with rural areas is overreaching at best and way-off-mark at the worst.
This reminds me of how you can make an X-Y chart prove a point by manipulating the scales. (I'm not trying to say the authors have done that, but the cause and effect connections I don't believe are warranted the way they have been presented.)
Referring to the National Geographic study synopsis:
"1. Cities Aren't Statistically More Dangerous."
Now, I'm not a statistics guru, but here the biggest problems are what is urban versus what is rural; And the other seems to be aggregating the whole country as one or the other. The study evidently uses counties as the geographic units.
Going back to the original study PDF (linked in the National Geographic article), maps are given, and I repeat a copy below. Take a look, for example, at San Bernardino County. It is shown as "urban." Anybody who's from Southern California probably will tell you that San B. County is HUGE. The only really highly urbanized part is adjacent to L.A. The side next to Nevada is totally rural. So the "population density: map is misleading for San B. County. There are plenty of other examples you can find yourself, I'd bet.
The other thing that strikes me about the "all injury death rates" map, where the "grain" of counties (the geographic size) is finer, you see marked regional differences. The "all injury death rates" are lower in the Rust Belt than in Dixie, for instance. Iowa & Nebraska are depicted as much lower than Alabama and Mississippi are.
Back to the National Geographic study synopsis:
3. Rural Areas See More Car Deaths Than Suburbs or Cities Do.
and –
4. Race Correlates to Injury Rates in Surprising Ways.
and –
5. Higher Education and Income Equals More Deaths.
Hum? Automobiles on high-speed roadways, maybe? The poorer people are less likely to be motoring all over the countryside, whereas people-of-means are more likely to do so. Rural areas are likely to have higher death rates in auto crashes I should think. The speed is higher, and in many western rural areas, you have more hills, curves and distance. But I'm not claiming the data demonstrate that. I just pose it as a possibility.
Anyway, the map —