The study looks at people over 55 years of age. It is possible that there is some sort of selection effect going on -- maybe decades of heavy drinking will weed out all but the most alcohol-resistant individuals, so that those who are still drinking heavily at 55-60 without ever having been harmed by it are mostly immune to the doses they're taking. From what I see, the study controls for past "problem drinking" (which they don't define precisely), but not for people who drank heavily without developing a drinking problem, but couldn't handle it any more after some point and decided themselves to cut back.

Also, it should be noted that papers of this sort use pretty conservative definitions of "heavy drinking." In this paper, it's defined as more than 42 grams of alcohol per day, which amounts to about a liter of beer or three small glasses of wine. While this level of drinking would surely be risky for people who are exceptionally alcohol-intolerant or prone to alcoholism, lots of people can handle it without any problems at all. It would be interesting to see a similar study that would make a finer distinction between different levels of "heavy" drinking.