So there are two discussions to have here, one of which is about radiation, the other of which is about nuclear power. It's fair to say that the two discussions are tied together by a lack of familiarity and yes, unfamiliarity breeds fear.
For background, I grew up in Los Alamos, NM, the second generation of my family to do so. My father has done radiation monitoring and dosimetry for the past 40-plus years, for the past 20 or so, with NEST. His father was involved in Project Plowshare. It's fair to say that I have the familiarity most people lack. Interestingly enough, my father and I disagree about nuclear power, but more on that in a minute. First, radiation and health.
Your linked article is about radiation, and whether or not we're irrationally afraid of it. This is a settled question: as a culture, we're irrationally afraid of it. The tableau of this question is a cave in Germany where people pay to breathe trace amounts of radon. WORTHY OF NOTE: the exposure described is under the levels at which people need to worry about exposure. Those levels are well-researched, at least in the "you're fucked" regime - the article discusses single-digit milliSieverts while "you're fucked" starts at double-digit Sieverts. Even in the context of "irrational fear", you're talking about alternative health treatments maintained within the known limits of safe exposure. This is sort of like homeopathy: at worst, it won't hurt you.
The therapeutic effects of radiation, on the other hand, aren't well studied at all. Wiki led me to this study, which I don't see anything obviously wrong with.
Wanna see how not settled the whole discussion of low-dose "radiation" is? Here's the Department of Energy, attempting to be clear:
All that to say, yes, low dose radiation risk is virtually impossible to quantify and low dose radiation benefit is virtually unstudied. Could we study it more? Sure. Will we? Not unless you have a radioactive cave you're trying to monetize. "Things that are radioactive" are bad to keep on the shelves because obviously, concentration matters and the workers who handle it get a lot more exposure than you do. Thus, medicinal radiation is mostly limited to aggressive cancer treatment and alternative health spas.
Nuclear power appears at first to be linked to these concerns. I'm not convinced it is. China is dealing with a full-fledged environmental apocalypse from coal but their future plans are only 3% nuclear. Most of our nuclear plants were built back in the '50s and '60s when the externalities could be easily masked. The best breakdown I've seen on the actual costs of nuclear power are by Bill Mckibben in his book Eaarth. Look inside starting on page 57. TL;DR: nuclear plants aren't being built because if they are completed on time and within budget, they pump power out at around 17-22 cents per kW/h, a figure that can be beat by pretty much everything else. Check this shit out:
If your choice is 7 cents per kWh for solar or 17 cents per kWh for nuclear, nuclear is a tough muffukin' choice to make.
And I think that is a fact nobody has wanted to talk about: nuclear is unpopular because it's too expensive at the best of times.
McKibben: Yeah, nuclear power, I mean—it’s just too expensive. It really isn’t going to happen. I wrote a big piece in National Geographic about energy in China, and even the Chinese, they’re spending more than anybody [on nuclear] and they’re saying it’ll be three percent of their electricity supply. It’s not viable. The really cool thing—here is a book to go look at. It just came out as a ninety-nine cent Kindle Single. It’s by a guy named Osha Davidson, it’s called Clean Break, and it’s about what’s going on in Germany, which is un-fucking-believable. Munich’s north of Montreal, and there were days this month when they got half their energy from solar panels. It has nothing to do with technology or location—it’s all political will, and they have it.
My father disagrees. He thinks nuclear power hasn't been widely adopted because of paranoia and fear. He's also the kind of guy who kept plutonium in the garage. But then, he hasn't looked at the economics, so far as I know.