A few years ago I owned such an axe from SE Denmark. The head was supposedly original 6000 years old. The knapping traces were indeed covered with white patina. The shaft was made according to neolithic finds. There was a golden printed certificate with it... Nevertheless, I own(ed) a lot of neolithic axes from the middle Europe and all of them are polished at least at the very edge.
http://i18.photobucket.com/albums/b1...ps0315e10b.jpg