After the recent earthquake in Japan, and the resulting problems at the Fukushima Nuclear Power Plant Ann Coulter took it upon herself to defend the nuclear industry with her report entitled "A Glowing Report on Radiation."  Here she is discussing it on Bill O'Reilly:

Now, here is what Ann writes about the New York Times has written, 

As The New York Times science section reported in 2001, an increasing number of scientists believe that at some level -- much higher than the minimums set by the U.S. government -- radiation is good for you. "They theorize," the Times said, that "these doses protect against cancer by activating cells' natural defense mechanisms." 

Among the studies mentioned by the Times was one in Canada finding that tuberculosis patients subjected to multiple chest X-rays had much lower rates of breast cancer than the general population.

The Times article she was citing is entitled "For Radiation, How Much is Too Much"

Now, some scientists even say low radiation doses may be beneficial. They theorize that these doses protect against cancer by activating cells' natural defense mechanisms. As evidence, they cite studies, like one in Canada of tuberculosis patients who had multiple chest X-rays and one of nuclear workers in the United States. The tuberculosis patients, some analyses said, had fewer cases of breast cancer than would be expected and the nuclear workers had a lower mortality rate than would be expected.

Dr. Boice said these studies were flawed by statistical pitfalls, and when a committee of the National Council on Radiation Protection and Measurement evaluated this and other studies on beneficial effects, it was not convinced. The group, headed by Dr. Upton of New Jersey, wrote that the data ''do not exclude'' the hypothesis. But, it added, ''the prevailing evidence has generally been interpreted as insufficient to support this view.''

So...there is that.

But what about those article Ann Coulter makes reference to?

A $10 million Department of Energy study from 1991 examined 10 years of epidemiological research by the Johns Hopkins School of Public Health on 700,000 shipyard workers, some of whom had been exposed to 10 times more radiation than the others from their work on the ships' nuclear reactors. The workers exposed to excess radiation had a 24 percent lower death rate and a 25 percent lower cancer mortality than the non-irradiated workers.

But the article, Cancer risks and low-level radiation in U.S. shipyard workers, did not quite come to those conclusions. Here are excerpts from its abstract:

Nuclear workers had lower mortality rates for leukemia and LHC than US white males but higher rates of lung cancer and a significant five-fold excess of mesothelioma...Except for LHC, these risks are not significant. However, the increasing risk with increasing exposure for these cancers, some of which are known to be related to radiation, suggests that low-level protracted exposures to gamma rays may be associated with these cancers. Other agents such as asbestos, which are common to shipyard work, may play a role especially in the risk of mesothelioma.

Ann then references a very unique incident in Taiwan,

In 1983, a series of apartment buildings in Taiwan were accidentally constructed with massive amounts of cobalt 60, a radioactive substance. After 16 years, the buildings' 10,000 occupants developed only five cases of cancer. The cancer rate for the same age group in the general Taiwanese population over that time period predicted 170 cancers.

 

The incident she is referencing was covered in the article Is Chronic Radiation an Effective Prophylaxis Against Cancer. It is true that the rates of cancer for those living in the buildings was lower than the national average.  However, the article has been criticized, and its authors even note,

Assuming the age andincome distributions of these persons are the same as for thegeneral population, it appears that significant beneficial healtheffects may be associated with this chronic radiation exposure

This is a fairly bold assumption to make when your the results of your claim go against the bulk of the body evidence that has been studied for the last century.  The rate of cancer does vary significantly among different categories of the population.  Differences can be found in income, race, socio-economic status, but most significantly, age.  If those living in the buildings we below 60 years of age, their rate of cancer would be significantly below the national average.

So, I think I have effectively shown some ways Ann Coulter is able to bend the truth to create the narrative she wants in her stories.  What she did to quite effectively was manage to change the narrative.  People in Japan and around the world are not afraid of the low levels of background radiation that surround us everyday, or even necessarily the small amount of radiation a plant can chronically leak.  More so, we are concerned with the catastrophic amount of life that can be lost and irreversibly changed when our safety is left in the hands of private business and underfunded government regulators.