You left out that oxidizers do not bleach without moisture.
Also you failed to mention that concnetration plays a role. If I dilute sodium or calcium hypochlorite down to the same concentration as Miracle-Mineral-Supplement then how similar or different are their actions? Miracle-Mineral-Supplement is merely a weak chlorite, which is very similar to a diluted hypochlorite.
Before you try to argue any further read the bottom of page 746 concerning chlorite and hypochlorite then try to tell me that I am wrong: