It's probably natural to assume that any approach such as AVRT that maintains that addiction is not a disease must then be saying that addiction is about willpower.
If you see someone drinking to the point that they are ruining their lives and the lives of other it's hard to make any sense of it other than to think they have a disease, in which case there's not much they can do about it, or that they are compelled by some kind of force in which case they are able to do something i.e. fight it by using "willpower".
If you think of willpower like this then it doesn't really square with the AVFT and the Big Plan. But another and probably more accurate meaning of willpower is that it's the power of choice and this obviously fits very well with this paradigm which sees drinking as something you choose to do and so can be stopped by choosing to do so.