So much denialism going on here, it's like talking to my alcoholic relative. This shouldn't trigger such a strong reaction, if it does, one should look into why that is.
I'm sure you wouldn't have seen anywhere near this kind of reaction if the headline was instead "Any level of alcohol consumption increases liver cancer risk by X in 10,000" or "Adjustments to confounding factors show that non-drinkers have a 0.0000X% longer life expectancy".
Beyond the headline designed to invoke a reaction, I think there's a good basis for general fear of this kind of judgment - it invokes the language around many other prohibitions of all that is good and fun in the name of our physical or moral health.
We are only just working through lifting prohibitions on Cannabis here in the west, albeit with many strings attached. Many countries (and a good number of North American counties) still have prohibitions on alcohol. We as a society prohibit many kinds of mushroom, plant roots, leaves and oils.
Here in Canada the health authority has a "no safe levels" attitude towards absinthe, house-made mayo, rare burgers and many of the world's greatest cheeses. We've put "for external use only" warning labels on cooking ingredients like mustard oil and tamarind extracts. We've banned cooking wines entirely!
So yes. When I see "no safe levels of alcohol" I do tend to over-react. Keep your grubby little hands off my bottle.