(Note: I don't know who Ann Coulter is. I can, however, comment on the generic claim that radiation is "good for you".)

There is empirical evidence that suggests that low to medium amounts of absorbed gamma radiation boosts immunity and resilience to ailments such as heart disease, though it may (or may not) increase rates of cancer. It has been suggested and that the reduction in the probability of death from other diseases offsets the increased probability of death from cancer.

The reference I found on this is [Lawrence Solomon's opinion piece in the Financial Times: Low exposure to the Nagasaki atomic blast resulted in longer lifespans][1], which states:

> The tens of thousands more distant from Ground Zero [of Nagasaki and Hiroshima], and who received lower exposures to radiation, did not die in droves. To the contrary, and surprisingly, they outlived their counterparts in the general population who received no exposure to radiation from the blasts.

and 

> The only evidence that exists as to the health of humans who have been irradiated at low levels points to a benefit, not a harm. Difficult though it may be to overcome the fear of radiation that has been drubbed into us since childhood, there is no scientific proof whatsoever to view the radiation emitted from the Fukushima plant as dangerous to the Japanese population

These findings are supported by (and reference) the paper "Mortality of A-bomb Survivors in Nagasaki and Hiroshima", by M. MINE, S. HONDA, Y. OKUMURA, H. KONDO, K. YOKOTA and M. TOMONAGA, [Atomic Bomb Disease Institute, Nagasaki Univ., Sch. Med., Nagasaki 852-8523, JAPAN][2]. This paper states:

> From the analysis of LSS’s population, RERF, lower relative risk of mortality from non-cancerous disease than control was observed for a dose range, 0.06-0.49Gy, when city was not adjusted. But when city was adjusted, lower relative risk was not observed. Although the number of subjects analyzed in Nagasaki University was smaller than that of LSS’s population, we have obtained the lower relative risk of mortality from noncancerous disease for male at a range of low doses.

These correlate with my undergraduate studies in physics and later work as a health and safety worker for Atomic Energy of Canada Limited (AECL). In undergrad I recall that [Marie Currie][3] and her husband wore on their arms slabs of radium and/or uranium because they were under the impression that the radiation these materials emitted boosted immunity. As a worker for AECL at a nuclear power plant, it was commonly accepted that [people working at the nuclear power plant on average lived longer than the general population and had lower rates of cancer][4] (Submission of Dr. Patrick Moore, Chairman & Chief Scientist Greenspirit Strategies Ltd. To The U.S. Nuclear Regulatory Commission Public Hearing on Potential Environmental Impacts From a License Renewal of Indian Point Nuclear Power Plant, dated September 19, 2007). From that reference:

> A 2004 Columbia University Study of 35,000 respondents concluded that “…nuclear power plant workers in the United States…live longer and have significantly lower cancer rates compared to the general population.”

Unfortunately I couldn't find offhand the 2004 Columbia University study or equivalent, and in any event I worked at AECL quite some years before 2004 (so the knowledge at the time wouldn't have been from that study). Nevertheless, that 2004 study would seem to support the assertion I've put forward.

All that being said, there are significant deleterious effects from radiation exposure. While the Curries strapped radioactive materials to their arms, they [suffered significantly for it][5] (Marie Curie: Pioneering Physicist By Elizabeth R. Cregan, p. 17).

While gamma radiation is, on the above basis, understood to have some benefits, the effects of [beta][6] and [alpha][7] radiation as are known to be quite destructive to cell tissue. While these forms of radiation are less common to be exposed to and easier to protect against than gamma radiation, I strongly doubt they've any positive effect at reducing the risk of cancer.

Going back to the claim that those around Fukushima are "much less likely to get cancer" seems overstated. While there are clearly health benefits, and the evidence is mixed about whether exposure to radiation increases or decreases risk of cancer, I feel it's reasonably clear from the evidence we have to date that the risk wouldn't be "much less", as claimed.

As well, on whether cells have a natural defence mechanism when exposed to low or medium doses of radiation: I don't know of any studies, nor do I have any other knowledge or information, that would support such a conclusion. That being said, I think it's perfectly plausible that cells could have such an ability.

  [1]: http://opinion.financialpost.com/2011/03/21/lawrence-solomon-reactor-victims-will-benefit-studies-show/
  [2]: http://probeinternational.org/library/wp-content/uploads/2011/03/MineIR10-JpSurvMort1.pdf
  [3]: http://en.wikipedia.org/wiki/Marie_Curie
  [4]: http://www.safesecurevital.com/pdf/Dr_PatrickMoore_Sept-07.pdf
  [5]: http://books.google.ca/books?id=W0S86P1-IyEC&lpg=PA17&ots=-idNOAW4WD&dq=marie%20currie%20strapped%20uranium%20to%20arm&pg=PA17#v=onepage&q=arm&f=false
  [6]: http://en.wikipedia.org/wiki/Beta_particle
  [7]: http://en.wikipedia.org/wiki/Alpha_particle