Yes, but first let's clarify what's being claimed.
There's a little confusion in the question (which is fair enough, it's a confusing topic). There's no doubt that ordinary CT scans and x-rays do lead to a small increase in cancer cases, it's measured, quantified, and taken into account by clinicians when making decisions, case-by-case, dose-by-dose. Many specific CT scans and x-rays are most definitely not what could be called low dose.
What is being doubted is the assumption that:
- The linear relationship between radiation dose and risk continues at very low doses
- That there's no threshold below which there's zero risk
- That it's therefore impossible to have a risk-free scan using extra-low doses of ionizing radiation. The authors argue that this is a very real possibility, while acknowledging the risks of higher dose scans.
It's all about the doses.
So, is there a linear relationship that continues no matter how low the dose, or could there be a threshold below which there's no risk?
This 2015 Nature article, summarising and discussing the context of a major study published in 2015 in the Lancet, seems the best up to date summary.
It shows that the linear relationship between dose and cancer risk does persist, even at absolutely tiny doses, with no safe threshold. It explains why there is controversy among researchers - it's very hard to measure the relationship at tiny doses, and this study only managed it by having access to very accurate data from 300,000 people.
Basically, before this study, you could make a case that there's no strong proof of a relationship below a certain level - but this study shows that this was simply because no study had been done at a scale that could detect such tiny increases in risk.
Researchers pin down risks of low-dose radiation
Large study of nuclear workers shows that even tiny doses slightly boost risk of leukaemia.
For decades, researchers have been trying to quantify the risks of very low doses of ionizing radiation — the kind that might be received from a medical scan, or... [other examples]. A landmark international study has now provided the strongest support yet for the idea that long-term exposure to low-dose radiation increases the risk of leukaemia, although the rise is only minuscule (K. Leuraud et al. Lancet Haematol. http://doi.org/5s4; 2015).
...it scuppers the popular idea that there might be a threshold dose below which radiation is harmless...
...it has proved extremely difficult to determine whether this relationship [between dose and cancer risk] holds at low doses, because any increase in risk is so small that to detect it requires studies of large numbers of people for whom the dose received is known. A study of more than 300,000 nuclear-industry workers in France, the United States and the United Kingdom, all of whom wore dosimeter badges, has provided exactly these data.
...The study confirmed that the risk of leukaemia does rise proportionately with higher doses, but also showed that this linear relationship is present at extremely low levels of radiation.
That last part is the crucial part.
Of course, we should be clear that we're talking about utterly tiny increases in risk here. If it sounds alarming, it shouldn't. I recommend this BBC article about radiation risk and bananas, which should help put into context just how small a risk a very low dose risk is.
And there's still a tiny amount of wriggle room for someone determined to argue that there might be some zero-risk threshold: this study was of repeat exposure to very low doses, and even these 300,000 people weren't enough to measure risk impacts of one-off exposures to very low doses.
But such a risk would be so tiny, it'd be almost impossible to measure - and this study shows that there's no reason to think there might be something special about very low doses that could enable such an exception.
