This is a myth. Yes, there is slightly more salt in the water but not at a level that will ever hurt a healthy human.
The salt is used to clean (ionize) the material which removes the particulate that makes the water hard. So, it's simply a flush and the softener will rinse the remaining salt from the system. How often the cleaning material needs to be cleaned is based on how hard your water is and how soft you want it to be.