Nope, it is a rumor. It would make your condition worse if you do so. The skin under your eyes is the thinnest part in your body. The sunlight would increase the level of melanin in your skin to make the skin darker, especially you exposure to bright sunlight. In order to reduce the dark circles under the eyes, you should intake supplement of iron in daily diet, because a deficiency of iron could cause dark circles under the eyes. And you had better wear sunglasses in the sun, which could prevent your dark circles under the eyes to become darker. What is more, you can place tomato slices over your eye areas due to it can lighten the skin.