It's an interesting debate.
Intuitively, I would agree with the hybrid approach of genetic contribution (in many, but not all) to addiction and the individual's ability to make a choice for him/herself (especially after learning of the possible genetic addiction).
However, I read an interesting article last month in Nature about how it is theorized that alcoholics/regular drinkers accrue what are called "silent synapses" in the part of the brain associated with episodic memory formation, and that these synapses are theorized to be correlated with how people respond to future cues to drink again. The more synapses you've accrued, the more sensitive you are to these alcohol cues (and thus the more likely you are to relapse).
Of course, this is all still being studied and nothing conclusive has been reached, and it doesn't remove moral agency or individual choice, but it does highlight just how stacked the deck can be on a chemical level, which does take some agency away.
I do think the moral choice paradigm is valuable, because it can be extended to almost every aspect of your life and help you make the sort of "backend" changes that can help you maintain sobriety. But of course it's also good to be open and aware of how others who suffer through addiction respond to that paradigm and what works for them.