I responded to that article since they are still missing some critical points. Yes it is true that in high bather load pools, especially indoors, there can be a buildup of Combined Chlorine (CC) that will not get oxidized readily by superchlorination. However, that isn't necessarily a real problem. The current commercial/public pool standards of <= 0.2 ppm CC are based on the presumption that higher CC levels mean more volatile and irritating disinfection by-products such as nitrogen trichloride or more volatile and carcinogenic disinfection by-products such as chloroform (and other trihalomethanes). However, that assumption is not correct, at least for nitrogen trichloride, since one can measure higher CC and yet have lower nitrogen trichloride because the active chlorine level is lower. The tradeoff is that other intermediates such as monochloramine, dichloroamine and chlorourea will be higher, but these are less problematic (i.e. less volatile, higher odor thresholds, not carcinogenic, etc.).
As for reduction of disinfection by-products, there are ways of reducing them and their precursors without having to resort only to water dilution. One can use supplemental oxidation IF such oxidizers actually break down the precursors and don't create worse by-products in doing so -- sunlight seems to work well for outdoor pools since it creates hydroxyl free radicals when it breaks down chlorine and these are very powerful oxidizers. One can also use coagulation/filtration techniques though that only works well with certain types of chemical compounds. The German DIN 19643 standard has a heavy emphasis on coagulation/filtration.
The Dupont Oxone product, which is the non-chlorine shock product we call MPS (short for potassium monopersulfate), is a selective oxidizer similar to chlorine but selective in different ways. It is good at oxidizing ammonia and can do so before chlorine so can avoid the inorganic chloramines. It has some oxidation ability against monochloramine, though not as much. It apparently is not much of an oxidizer for urea which is unfortunate though Dupont didn't look at actual pool water so it might have some reactivity via catalytic pathways (i.e. in the presence of metals). MPS does react with amino acids and other compounds. The good news is that it does seem to react to many compounds that chlorine reacts with, but does so more quickly so it can prevent at least some of the disinfection by-products, but mostly as a preventative being present in the water along with chlorine. To use it after the fact when DBPs are already present is not as effective.
Oh, and by the way, when we shock the pool on this forum when there is CC, we have CYA in the water where the shock level of an FC that is 40% of the CYA level is equivalent to 0.6 ppm FC with no CYA. So it isn't going to be producing as many disinfection by-products as quickly as most indoor pools that have a higher FC and no CYA. Our shocking usually doesn't result in CC persisting, but that's largely because the pools are outdoors so the sunlight helps in producing hydroxyl free radicals. In fact, the shocking raises the pH and it is hypochlorite ion that is more sensitive to chlorine breakdown and that level goes way up sort of like super-charging oxidation. So while we wouldn't want the pH to get excessively high for killing algae or for creating scale, the higher pH is good for oxidation if the pool is exposed to sunlight.