He doesn't mention that carbon directly fights diseases but as medication removal. I'm not aware of carbon to directly fight any diseases. If so, would like to see the basis for it.
Activated carbon removes organics from the water column; phenols (how often do you get to use that word), proteins, acids, and other organic molecules produced by the livestock. Similar to and normally used in conjunction with skimmers. Nitrate/phosphate and alkalinity/calcium are not affected. The pathogens are simply not absorbed due to the mechanism of how carbon works (not a chemist here).
There could be a case that these organics could aid in some bacteria/disease spread but in my mind that's even more of a case to use as a prevention and not as a treatment.
Of note, GAC hasn't been found to remove excessive amounts of trace minerals (in my case, based on my last ICP testing and running carbon from day one - my trace elements are just fine). Lastly the nitrifying bacteria on carbon media will exist but should be minimal and not impact tank by removing. Everyone cleans/replace sponges/filters all the time with no effect.