I asked this question to Angela White of Breasteeding123.com and she has prepared a wonderful answer on her blog. With her answer, I now feel more confident about AP. I like this part of the answer:
When children create a healthy attachment to their parents, they feel more confident and secure. With that self-assurance, children feel free to explore their world, becoming more independent because they know that they can return to the security of an attached and loving parent.