In short: No. But it is a bit more complicated than that.
It is probably a bad way to phrase it like "The more alcohol a society consumes, the fewer alcohol-related problems and alcohol-related deaths (including cirrhosis) it has, […]"
This is likely to be a journalistic creativity that as usual cannot make head or tail of the logic of an argument.
If you phrase that statement into:
"The pure correlation between high amount of alcohol consumed in a society and alcohol-related problems in such a society is surprisingly low, speaking against the probability of any unconfounded causal relationship." We then come closer to the findings gleaned from cross-cultural studies.
(http://www.peele.net/lib/sociocul.html Alcohol and Society.
How Culture Influences the Way People Drink)
Or, as the journalist easily could and should have phrased it: Alcohol problems are not simply a result of how much people drink.
To make it clear: Consuming alcohol in small amounts seems to be more beneficial than living completely abstinent. Overdoing alcohol consumption will quite quickly lead into the realms of undesirable effects and consequences.
This is a clearly and quickly demonstrated direct relationship: put a funnel in your mouth, drink one too many over your established breaking point and observe the unpleasant results.
But this is not only different in an inter-individualistic perspective but it seems also to be codependent on the way a surrounding culture handles consumption of alchohol in general.
Drinking 2l of wine a day is probably not so good, even for a Frenchman in France. But taking all those Frenchmen who do so and comparing this group to all Americans who do likewise indicates that the Americans drinking that much will have more alcohol related negative consequences on their list of complaints.
Now there is the argument that overall diet may further confound these findings, since the French or Italian diets are generally considered much healthier than 'the' American diet. Also there is a differing preference in the type of beverage preferred (wine vs hard liquor).
But looking through the available data in comparing different countries and their differing cultures seems to produce a much stronger predictor for probable outcomes:
The cultural drinking patterns put into a continuum from integrated drinking to ambivalent and unintegrated drinking.
A puzzling factoid to this is the phenomenon that those negative outcomes apply to both levels of social and even biochemical effects.
To grossly oversimplify these things in hope of illustration: That means drinking beer for breakfast and together with other foods, continuing drinking over the course of the day in small doses but arriving at a solid buzz in the evening in a society where this is the norm or at least accepted behaviour is less damaging than doing this exact same thing in a society where this is heavily frowned upon. The effects of wanting to consume the equivalent same amount of pure alcohol in the form of whiskey after a long workday of puritanical abstinence should be self-evident. But it again still does make a difference in terms of expectable outcomes in regard to the societal acceptance of that behaviour.
Further, the data seems to indicate that in those countries with the most healthy attitude towards drinking alcohol the people did not necessarily just consume more alcohol than other countries: It's more of a finding like: look how much they they drink and how surprisingly 'healthy' they still are.
Alcohol can be very damaging. The way too many countries handle it through demonization makes things much worse.
Albert D. Ullman First Published January 1, 1958: Sociocultural Backgrounds of Alcoholism
Late-life alcohol consumption and 20-year mortality.
R Room, K Mäkelä, : Typologies of the cultural position of drinking.
M. Astudillo, S. Kuntsche, K. Graham, and G. Gmela: The Influence of Drinking Pattern, at Individual and Aggregate Levels, on Alcohol-Related Negative Consequences
The Influence of Drinking Pattern, at Individual and Aggregate Levels, on Alcohol-Related Negative Consequences