Children with parents who are always out working are not able to develop such strong attachments with them. Though the nanny may often replace the parents role as the caregiver of the child, sometimes they do not. However, less attachment with their parents at such a young age does not necessarily lead to the child living a live of negative results since they were not able to establish the secure attachment.
This is true, the role of caregiver may not necessarily be the mother or the father. Sometimes it is the grandmother, the nanny, or someone else if the mother is too busy. At the same time though, they did attach or form that bond with the person taking care of them, in my opinion. I feel that they still get attachment just the social role of the person giving it to them changes. I think that the attachment theory is not very detailed in this, an it is a very interesting limitation of the theory.