I agree it is hard to understand, and without going into the chemistry it's hard to explain further, also I'm no expert, I'm only going on what sources of information I could find.
Chlorine dioxide does have a unique oxidizing ability due to it's chemistry but that doesnt make it safe.
As a gas, ie when not dissolved in water, it can be particulary harmful to the lungs, so it's not as safe as Jim Humble claims, infact some Miracle-Mineral-Supplement sites have been suggesting inhalation which is very irresponsible
At high enough levels it can damage cells but it has been shown to be very effective at killing a wide variety of single celled organisms and viruses at much lower levels than other oxidants so making it safer at least when in dilution.
Like I said I'm no expert so if your interested I suggest you look into it further yourself