“does not alone explain” means the same thing as “cannot be explained by.” I think your confusion stems from “is influenced by” being a much weaker statement than “can be explained by.” Being in prison for example isn’t ”explained by” people breaking the law as that would require nobody to be falsely imprisoned or be set free on a technicality etc.

The second statement follows from the first. If you can’t completely determine someones wealth from past decisions alone, then you can’t group the poor or wealthy by the history of their past decisions.