I think Kate managed to get away with passing of Aaron as her own due to the time difference on the Island, whilst time was looping, noone on the island aged, whilst the outside world carried on as normal. So Kate would easily be able to pass off Aaron as her own child, conceived and born on the Island. I'll bet at some point, someone from Hanso will, question how Kate managed to do this, as we all know you cannot conceive and give birth if it happens on the Island. That's also why we know that sun's baby is not Jin's, big clue in this epi.

__________________
Baby I am tied to a tree in a jungle of mystery. I just got tortured by a damned spinal surgeon and a genuine Iraqi. 'Course I'm serious.