I think that a possible alternative explanation for the correlation depends on the number of children a family has. For the first child, the parents would be more likely to spend time with him or her because it is their first child. For example, parents tend to take less pictures of their second child than their first. So the number of children that parents have can play a part in how their children develop their attachments.
This is definitely insightful and makes sense logically; I've also noticed attachment styles differ a lot between an only child and a child in a large family. Generally what I've observed is that an only child will require more attention to be satisfied than the latter; this can be explained by their early attachment - both parents probably spent a lot of time with the child and were frequently interacting with it. I think this goes along well with what you're saying.
This argument brings up a good point that I didn't particularly have, but nonetheless is pretty valid because the amount of attention a child receives comes to shape a child quite drastically, for he may be more or less social with other people based on his upbringing. I took a different approach in that I believed that the environment and social class played large roles in how a child develops. Nonetheless, our two opinions converge on the idea that the things and people around a child play large roles in children's development.
You bring up a good point that I did not consider when thinking about this question. I thought that the security within the household played a large role in a child well being. Things such as good schooling and a good home environment affect people a great deal. I think both of our points are valid and both impact children to determine their well being later in life.