I'm sure that's a factor, but it seems unlikely to me it's the only one. All else being equal, going through a repetitive cycle of pain/craving and relief throughout recovery seems likely to encourage addiction as well. Which of course isn't to say that everyone who experiences that will become addicted, or that those who do won't skew toward those who are facing other difficulties in life, but from what I've read it does have an effect. And it fits my common sense, not that one should rely on that in absence of real evidence.