Yes you have a valid issue. I operate a powder coat system in our plant. It certainly appears that they painted over the original black color.
Contrary to a previous poster you CAN powder coat over existing paint. The issue is that the cured powder will not adhere to surface with any durability, hence the chipping. IF they blasted the frame there would be no traces of black around the edges and chip marks.
Chipping in large areas like what are pictured are a result of either a poor prep job of the surface, baking the powder for longer then needed (brittle) or they simply shot powder over existing paint.