I peel mine nowadays. The skin and eyes are where most of the nightshade toxin is and potatoes don't bother my arthritis as much if I don't eat the skins.
But, in principal yes, skins. Sometimes I would make mashed potatoes with the skins left on. I have even put them through a food mill with the skins on. A lot of the skins stay in the food mill, but there are little brown spots of skin in the mashed taters.