While i think there is a correlation between secure attachment and later well-being I think it can not be a cause and effect relationship. There are too many factors that contribute towards one's well being. For example, while a child can have secure attachment to their mothers or parents as well, they can be brought up in a school or with friends that are either brought up in well-to do homes or ones where the children are not so fortunate. These influences by people outside of immediate family members can lead to different outcomes. I think financial status, peers, exposure to media, etc are a few of the factors that can lead to someone's well-being or not well being even if they have secure attachment as a child.
I agree that although there is a correlation between secure attachment and one's future well-being, it is not a cause-and-effect relationship due to the large amount of possible variables. Other factors might include one's temperament, education, or even genetics. The media is a valid factor that I had not considered, but could definitively influence one's future well-being.
So you're basically saying that a child's environment is also another factor? I would agree there with you, but I don't think it plays nearly as big of a role as secure attachment in determining later well-being. Though I do think by adding in financial status, peers, exposure to media, etc, we are coming to a more complete picture.