I've raised soft water fish such as geos and discus in normal household tap water for years and have never came across this problem until now. I do have a ro/di unit that I'm thinking of putting to use now mixed with some tap water. Both my vieja and geos along with true parrots are all showing they have HITH so both hard and soft water fishNatural soft water is different from softened water. Natural soft water such as black water has high tannic acid, near zero hardness, and low dissolved ions with conductivity under 100. Household softened water is an ion exchange process that replaced calcium with sodium. The resulting water, though low in hardness, is high in dissolved sodium with conductivity in the 1000s, To replicate natural soft water, you have to mix in with DO or rainwater, or filter with peat to remove ions and add tannic acid.
The pathogens that cause HITH are ubiquitous and opportunistic ,depending on the fish resistance and environment conditions. I don't know why hard water fish are more resistance to HITH than soft water fish. If you medicate your fish but don't change the water chemistry or environmental conditions, even if you can achieve temporary cure, your vulnerable fish will be reinfected and you are wasting your effort.