Technically Miracle-Mineral-Supplement does kill pathogens. Scientifically it rips their molecules apart by aggressively kidnapping their electrons. That clearly indicates that the pathogens would be destroyed.
I think he means to go a bit farther. The pathogens would not be there if the immune system were strong in the first place. Some part of the immune system became weak. The liver? Some gland? Your skin tissue? You know.
The purpose of Miracle-Mineral-Supplement is to destroy pathogens, or enough of them, to give the immune system the upper hand (an advantage). Then the immune system can cure you; not Miracle-Mineral-Supplement .
I suppose the question becomes, "what can make the immune system strong enough to fight such diseases." I hope better minds will address this.