I agree with @Kevin - there are no ultimate statements in science. The answer is 'its all relative'.
With radiation and risk, more radiation means more risk of cancer or any number of other types of damage that can result. The question is is this significant? And this is a somewhat subjective question.
When someone says:
'there is no health risk from XYZ'
what they mean is..
"to the extent that we can determine, we can't see any more chance of adverse health if you are exposed to XYZ conditions than if you weren't"
DNA damage happens all the time. The frequent flier study you cite is trying to see if the additional exposure to cosmic radiation while flying, which is largely blocked by the atmosphere, causes a change in the rate of some cancers.
Radiation and cancer is like a lottery. If you buy just one ticket you might win. If you step outside, the thousands of extra gamma rays you get outside might start a cancer that will eventually take your life. If you buy 20 million tickets you will very likely win. If you hang out next to high levels of radiation, even for a short while, you will get so much damage you will not live long.
Its difficult to study the effect of low levels of radiation. The lower the levels of radiation we are asking about, the longer you will have to wait to see if there is an effect. If 10% more people get cancer, you have a very real concern that some of these folks might have done something else, like sunbathe or live in a poorly ventilated basement for too long.
The real question is, what is significant? I once saw a 60 minutes segment where a dermatologist said that she simply never directly exposes her skin to direct sunlight. I'm betting she never got a melanoma. She carried a parasol and wore light gloves outdoors. (sorry I can't find the link) She was at least in her 50s and she had the skin of a teenager. I still go out in the sun. I assume my risk of melanoma is 5-10 times more than hers was (this was a pretty old broadcast). (mine is 0.03% in the next 5 years btw). Its just not worth it to me.