My eldest daughter was the possessor of an 'outie' - I believe it's down to the way the chord is tied at birth, but afther the birth of her baby, it became an 'innie' - she doesn't really know when the change took place, being more occupied with other matters at the time, and I have no idea why the change occured, unless the natrual tautening of the area caused by pregnancy had that effect.
The cord isn't tied at birth. it is merely snipped off (had 4 kids, I've watched) What is left is just a kind of scar and all scars heal differently. When i was a child my navel stuck out. As i got older and a little fatter, it moved inwards, but if I so desire, i can still pull it out to clean. When i was pregnant, my navel stuck out again, so i'd really say it was down to body fat.