My opinion is addiction proper makes no distinction between the rich and the poor. Society itself makes a distinction of class between wealth and poverty, and this existing class distinction is applied as a stereotype that wealthy people have a 'different kind' of addiction challenge than do those in poverty. For me, this kind of reasoning is more about society and less about addiction.
An addict / alcoholic is an addict / alcoholic rich or poor an addict / alcoholic all the same.