Air pollution or eating wheat significantly shortened life expectancy?

A recent study linked air pollution to shorten life expectancy. It is probably true except that I found the argument very weak. The authors used data from China and found that the life expectancy is five and half years shorter in the north than in the south. And it argued that for decades (1950 to 1980), a government policy provided free coal for heating, but only in the colder north; researchers found no other government policies that treated China’s north differently from the south; therefore, air pollution must have been the culprit.

However, the authors did not mention that the same policy in the same period also provided rice for the south and wheat for the north as the main staple of food. I am quite surprised that nobody told the authors since anyone who lived in China during that period should have known. I left China in 1988 and for every month since I was an adult, I collected about 10 kilos of rice per month (government issued ration coupon). Since I could not eat that much rice a month, I used to exchange the coupon for eggs in the black market. People in the north got about the same amount in wheat flour. It is true, there was very little migration as the authors stated, since migration was strictly controlled. 

In addition to government policy, the eating habit was very different as well. There was very little availability of green leafy vegetables in the north. There were other vegetables, such as Napa cabbages, eggplants, carrots etc., but almost no green leafy vegetables.

I am sure air pollution poses health risks. However, I could have used exactly the same data from China and concluded that eating wheat or not eating green leafy vegetables shorten life expectancy.