I think one explaination is that when infants have a secure attachment, they develop their confidence at a younger age. By having a secure attachment, the infant is gaining the confidence to not only explore their surroundings but they are also gaining the confidence to do it in the presence of their mother. I think this confidence that is developed so early makes the child more attractive to others later on in life and less likely to develop social anixety.
I basically agree with your statement but the confidence is a slippery slope. One bad relationship may ruin the child's confidence all together. The mother's job is to comfort the child and create a strong and secure first link and guide him or her to create other positive ones.
I think that confidence is something that develops over time. It is a bit hard to assume that an infant, primarily exposed to their relatives and perhaps one babysitter, would be able to exhibit something similar to the confidence we identify in our peers. The presence of the mother, in my point of view, serves to establish a ground of safety as the child explores. Exploration leads to the understanding of the child's environment and perhaps, given enough time, will develop into confidence and self-esteem as the child grows. It is not so much the establishment of confidence but the willingness of the child to "survey the land" that arises from infancy.