Remember that just as photos of Alexandra, aimed for public consumption, were touched up to make her look less worn, it's very posible an occasional Grand Duchess blemish may also have been airbrushed.
Good complexions are influenced by a number of factors, including exercise, diet, heredity, hormones, sleep (or lack thereof), hygience, emotions, and stress. When I was an adolescent I had horrible skin, despite the fact that I cleansed it regularly. Ultimately medication helped to modify the problem, as did getting older (alas!) plus learning to deal a bit better with stress.