That policy means that the sheet metal used for the manufacture of their airplanes is made to special order, and expensive measures apply to protect those skins during manufacture.
The only "special skins" American Airlines required were those used on their A300-600's because Airbus does not used Alclad skins. If you look back their first AA A300's were painted gray and looked like c..p. American made Airbus change to Alclad skins for the remainder of their order.
Boeing uses Alclad skins on all their models (except the 787), regardless if they are polished or painted.
All aircraft skins are protected during the manufacturing process to prevent scratches as scratches can lead to corrosion and or fatigue cracks.
Lots of information on Alclad aluminum on the web but basically it is a thin layer of pure aluminum applied to both sides of aluminum sheets. The pure aluminum makes up approximately 10% of the total sheet thickness and provides corrosion protection.