While attachment style seems to have a correlation with well-being later in life, the two may both be influenced by experiences with the parent. A parent who is loving and promotes a trusting relationship with their infant will likely cause that infant to become securely attached. As the child grows up, he or she may perform better in life because the parent's support and affection built the child's self-esteem and confidence; therefore, the child will be more confident in his or her self and abilities and foster relationships with others that are similar.
Conversely, if a parent is negative and does not encourage the child to explore on his or her own, this child may show anxious attachment. As the child grows up, he or she may not be as emotionally healthy or professionally successful because he or she never gained the confidence to pursue success independently.
I think that the correlation between attachment and later well being is directly and explicitly influenced by the interaction with the parent. I feel like the parent definitely has the influence on whether or not the child's positive attachment comes to fruition. Regardless of external factors, it is the parent's obligation the ensure that the child's potential for attachment and well-being is reached, and in this respect, I agree with you.