OK, then I will disagree even more. lol I thought that was just your shorthand for hydrogen peroxide.
The small rise in O2 when using hydrogen peroxide is not likely to be what reduces organics in the water. Hydrogen peroxide is much more reactive than the small amount of O2 that forms from hydrogen peroxide breaking down to O2.
Mechanistic studies of hydrogen peroxide oxidation of organics do not typically involve formation of O2, with the O2 doing the oxidizing of the organic.
For example, this paper shows that hydrogen peroxide combines with bicarbonate to form peroxycarbonate, and it is that peroxycarbonate that proceeds to react with carbon-carbon double bonds (typical yellowing compounds in a reef tank).