here:
http://community.seattletimes.nwsource.com/reader_feedback/public/display.php?thread=85219&offset=0#post_245768 ?
I think what the chemistry teacher is missing is the "By utilizing ion permeable membranes" comment (which allows them to separate the alkali and acidic solutions as the current is put through the solution), and the teacher is also assuming the equilibrium state of the final mix - the article says "Electrolyzed water loses its potency fairly quickly, so it can't be stored long", which I think acknowledges that in the end you get what he thinks you would.
But at first you have hypochlorous acid, which, as the CTO claims, is widely acknowledged as the thing which actually disinfects:
Factors Influencing Chlorine Activity
Water pH
When sodium hypochlorite is added to water, it forms sodium hydroxide (NaOH) and hypochlorous acid (HOCl). All three forms of chlorine produce hypochlorous acid (also called available chlorine or active chlorine).
Hypochlorous acid is what kills pathogens. In high pH solutions, most of the hypochlorous acid disassociates to form hypochlorite ion (OCl-) which is not an effective sanitizer. Testing kits for free chlorine measure both hypochlorous acid and hypochlorite ion and alone do not indicate the quantity of available chlorine that kills pathogens. Chlorine solutions with pH above 8 are relatively ineffective against pathogens. Below pH 6, chlorine is more corrosive to equipment and activity is rapidly lost.
A pH of around 7 will maintain about 80% of the chlorine in the available (hypochlorous acid) form with very little gas formed (Figure 1). Thus, in order to know the sanitizing strength of ones chlorine solution,
both pH and free chlorine must be measured.
Both water source and form of chlorine used will affect pH management. Fresh water in Florida may have a pH above 8.0 due to dissolved calcium carbonate. Adding either sodium hypochlorite or calcium hypochlorite will increase pH, while adding chlorine gas will decrease pH. After adding commercial chlorine, adjust the pH of the water to 7 by adding either acid or base. Muriatic (HCl) or citric acid are commonly used to lower pH while sodium hydroxide (lye) will raise pH. The pH of water can be determined by using an electronic pH meter.
http://edis.ifas.ufl.edu/CH160(bold is in the original; I'm not trying to shout at anyone here)
What the electrolysing apparatus achieves is the same as adding sodium hypochlorite and hydrochloric acid to pools etc., in a convenient form.