More specifically, Barkskin provides an *enhancement* bonus to your existing Natural Armor, so an application of Mage Armor and Barkskin not only work together, but would also both benefit your Animal Companion, for example.
Nefreets observation may seem trivial and inconsequencial, but it is of a very big importance. There are several ways for characters to gain actual natural armor. And that would indeed stack with the "enhancement" bonus to natural armor from Barkskin. And as said before Mage Armor is an entirely different bonus that would indeed stack with barkskin (although not with any actual armor)
