Already slight dehydration can cause headaches - and yes, Miracle-Mineral-Supplement probably does have this effect as I can tell from my own experience. Additional water intake helped - that had already been observed by Jim Humble.
I could see a number of reasons :
The Miracle-Mineral-Supplement solution and its reaction products (salts) can slightly change the osmotic pressure environment in the intestines. That could lead to withdrawal of water from the body into the intestines and in cases of highly hypotonic solutions even to osmotic diarrheas (http://en.wikipedia.org/wiki/Diarrhea). But of course you may already lose water in this way without experiencing a diarrhea. Softening stool is a possible indication.
Further some reaction products of NaClO2 and CLO2 are chloride ions and chloride salts, which I believe are highly hygroscopic (http://en.wikipedia.org/wiki/Hygroscopic) and may bind water molecules in one or the other way inside the body.
Then, when pathogens are killed off in the blood and body tissues, this will result in cell debris which the body may try to flush out.
However these are only assumptions, I could not cite any formal study.