You need to go back and revisit your chemical reactions again...
In an open system, you are correct. However, in a closed system the chlorine dioxide reduces to mostly chlorite and some chloride. In a closed system no chlorine is released.
While Miracle-Mineral-Supplement is somewhat scary, you should check into Jim Humbles recommendation of using calcium hypochlorite (MMS2). It seems that chlorinating your colon is Jim Humbles answer to defeating illness... [note of sarcasm icon]