The journalistic version:

[T]hose who abstain from alcohol tend to be from lower socioeconomic classes, since drinking can be expensive. And people of lower socioeconomic status have more life stressors [...] But even after controlling for nearly all imaginable variables - socioeconomic status, level of physical activity, number of close friends, quality of social support and so on - the researchers (a six-member team led by psychologist Charles Holahan of the University of Texas at Austin) found that over a 20-year period, mortality rates were highest for those who had never been drinkers, second-highest for heavy drinkers and lowest for moderate drinkers.

The abstract from the actual study (on "Late-Life Alcohol Consumption and 20-Year Mortality"):

Controlling only for age and gender, compared to moderate drinkers, abstainers had a more than 2 times increased mortality risk, heavy drinkers had 70% increased risk, and light drinkers had 23% increased risk. A model controlling for former problem drinking status, existing health problems, and key sociodemographic and social-behavioral factors, as well as for age and gender, substantially reduced the mortality effect for abstainers compared to moderate drinkers. However, even after adjusting for all covariates, abstainers and heavy drinkers continued to show increased mortality risks of 51 and 45%, respectively, compared to moderate drinkers. Findings are consistent with an interpretation that the survival effect for moderate drinking compared to abstention among older adults reflects 2 processes. First, the effect of confounding factors associated with alcohol abstention is considerable. However, even after taking account of traditional and nontraditional covariates, moderate alcohol consumption continued to show a beneficial effect in predicting mortality risk.

(Maybe the overlooked confounding factor is "moderation" by itself, and people who have a more relaxed, middle-of-the-road attitude towards life's pleasures tend to live longer?)