Brendan Koerner's article on why AA works has kindled a spirited convo in the 'sphere. If you are interested in this discussion, I'd recommend Gene Heyman's thorough 2009 book Addiction: A Disorder Of Choice, which discusses many relevant ideas.
One of his insights, that could answer the question posed by the article, is that choice-oriented rehab programs, like AA, "produce positive outcomes by enhancing the value of activities that compete with drug use and have developed effective techniques for encouraging hope in a brighter future."
To Heyman, one of the key distinguishing features of addicting substances is that using them makes other activities less rewarding. So, initial use leads to an increased preference for repeated use, in a downward cycle.
AA works because "just as heavy drug use initiates a downward spiral of increasingly negative consequences and decreasing options, healthy alternative activities can set in motion an upward spiral of increasingly positive consequences and increasing options."
Heyman also offers one of the most coherent explanations of voluntary behavior I have seen. His three principles for voluntary behavior are that 1) Preferences are dynamic, so that current choices alter the values of future outcomes, 2) Agents can choose between options one at a time or turn one-shot choices into sequences and choose among those (i.e., there are local or global choices), and 3) Individuals choose the best option.
Note that within this theory, certain voluntary choices can be quite self-destructive, as the best option in the short run (local) could be rather hazardous in the long run (global).
The theory has broad explanatory power. For example, consider the common tendency to justify drug use as the "last time." This makes sense because, as Heyman notes, "from a local perspective, the drug is the best choice; but from a global perspective, abstinence is the best choice. The ideal solution is to somehow do both.... If the situation can be framed as the "last time", then the dilemma dissolves. The same reasoning applies to "special occasions.""
Of course this choice theory can't explain all of the individual variance in outcomes, and its explanations break down particularly often when there is co-morbidity with other mental illnesses. But for choice to not get any play in an article like Koerner's is, to me, ridiculous.
If you don't feel like shelling out the $21.56 + S&H for Heyman's book, you might consider perusing an article of his (pdf) that touches on many of the same points, including the crucial local vs. global distinction (figure 4, p 113). But do also consider the book, which Ryan Holiday called "fascinating" and which Tyler Cowen said he "couldn't put down!", although they both ultimately hedged, for reasons which it is their voluntary choice to withhold.