I'm just not sure that putting roots that were rotting from too much water into noting but water is likely to solve the rot problem. Perhaps the person meant for you to remove all of the roots and put the stem in water, so that it could sprout a whole new root system. I honestly don't know if that works with Peace Lilies or not.
"As far as watering is concerned, Peace Lilies prefer an evenly moist soil. Most people find that they can water their plants once a week, depending of course on light and temperature conditions. At lower light levels or cooler temperatures, any plant will use less water than when it is more actively growing. Use room temperature water. Soil should never be soggy, and plants should never stand in a saucer filled with water. Peace Lilies should also never be allowed to completely dry out, which will result in wilting of the plant, death of the tiny root hairs which conduct water to the plant, and subsequent yellowing or browning of the leaf edges. Peace Lilies do exhibit a sensitivity to chlorine in the water, so in metropolitan areas where it may be heavily chlorinated, it's best to allow the water to stand overnight to allow the chlorine to dissipate before watering the plants." [Emphasis mine ... K]