There is a common misconception about "Salt Water" pools. There isn't much difference from that to putting liquid chlorine or tablets in. There is still Chlorine in your pool. The process in a salt pool works like this. As the water passes through the cell electrolysis breaks apart the salt in the water into it's basic components, sodium and chloride. The chlorine gas produced is that does the work of sanitizing the water. During that process the two elements re-bond into salt and the process starts over.
Typically there is a lower average level of chlorine but it's still just chlorine. That lower average may help to reduce the harmful effect that chlorine can have but it is still present.