Correct. Characters take on their look through changing the morph dials. Your textures are just that-- textures, and will not change, say the shape of the face. The reasoning behind "parenting" an object or prop is to keep it "stuck" on the character through turns and twists and general posing. You have to first position the prop where you want it, and then parent it. You can still move it after you parent it, but if you move the hand the ring is on, the ring will stay in place on the hand.