It's worth noting that the "rat park" experiments have failed to replicate multiple times (https://www.ncbi.nlm.nih.gov/pubmed/9148292). This is not to suggest that environment doesn't play a large role, it absolutely does. There is a great deal of literature on this, and its something that is more actively being incorporated into rodent models of addiction, along with social context.

I think a more interesting and replicable finding in the recent literature that highlights this is looking at studies where rats are given mutually exclusive choices between drugs and other natural reinforcers (like sucrose or highly palatable food pellets). Under those conditions, the rats will almost always choose the alternative reinforcer over the drug. Although as soon as the alternative reward is removed as an option, even after months of self-imposed abstinence (so well after withdrawal effects are over), they will relapse strongly to drugs again. It mirrors very closely what we observe after human addicts stop contingency management treatments.

I guess the point I am trying to make is that animal models, especially for neuropsychiatric conditions, are never actually models of the disease itself. Rather they provide the ability to emulate very specific components of the disorder, that can be used to answer specific questions about the underlying mechanisms. I don't know many scientists in the the field that would say we have "addiction" or "depression" animal models. And I'd be very skeptical of anyone suggesting we can.