I'm much like Nemmi.
I think we can get too caught up in the labels that come with parenting, esp AP. I don't subscribe to every tenet of AP but I try to follow my natural instincts with DS. I have a few select books and websites that I go to for info, as I regard 'parenting' as a life long skill that you need to be constantly studying for, IYKWIM.
As a few previous posters mentioned, AP is definately not permissive parenting. To be honest, at times I think to myself how easy would it be to put DS in time out, instead of talking to him about his feelings etc, but at the end of the day it wouldn't sit right for me.
I think you need to do what feels right for you and your child. There are no two family dynamics that would eveer be the same so follow your instincts.