You are quite right. Chlorine is one of the halogens that will displace iodine; and why we need to continue to supplement with iodine.
Try to keep remembering that:
"Chlorine dioxide and chlorine are not the same. Chlorine is a chemical element. In ion form, chlorine is part of common salt and other compounds, and necessary to most forms of life, including human. A powerful oxidizing agent, it is the most abundant dissolved ion in ocean water, and readily combines with nearly every other element, including sodium to form salt crystals, and magnesium, as magnesium chloride.
Chlorine dioxide is a chemical compound that consists of one chlorine ion bound to two ions of oxygen."
This is almost like saying the hydrogen and water are the same thing. If you forget this, you will understandably avoid Miracle-Mineral-Supplement . Me too.