Sounds to me like your watering technique is all wrong. The advice you have read about overwatering is more to do with the frequency of watering, not the amount. You should saturate the roots thoroughly when watering, until there is plenty of run-off. If you don't give the plant enough water to work with, it can't maintain it's structure properly, and roots and foliage will die off.
Use a proper wet-dry technique, where you drench the soil fully, then allow it to dry out until it feels light before watering again.