Depends on your local döner supplier’s supplier. I’m pretty sure my lamb döner doesn’t contain chicken skin, unlike the cheap “Drehspieß”.
For reference, there was a legislation set in place thatandates that a real “Döner” has to contain a certain amount of quality meat, otherwise it can not be sold under that name.
Then it legally couldn’t be called Döner and your Dönermann is lying to you.