Google dictionary defines "fertilizer" as "a chemical or natural substance added to soil or land to increase its fertility". It also defines organic as "of, relating to, or derived from living matter". Sticking by those two definitions, organic fertilizers don't necessarily have to contribute to the problem of runoff; you can simply rely on organic inputs that aren't water soluble and limit the use of ones that are. But since these non-water-soluble, organic inputs to your garden (read: plants, manure,
compost, etc.) typically attract beneficial microbes to your soil, then it sort of becomes apparent that instead of "organic" vs "non-organic", or "good soil" vs. "bad", the real contrast seems to be farming with a reliance on "water-soluble" vs "non-water soluble" inputs.
So what are the differences between water-soluble, organic fertilizers and water-soluble, chemical fertilizers? I believe the main difference is that water-soluble, organic fertilizers release their nutrients at a slower rate than chemical fertilizers, which makes for a less dramatic impact on the environment they're introduced to. Water-soluble, organic fertilizers also have less of a negative impact on soil microorganisms. I would say the long term effects of using water-soluble, orgnaic fertilizers in the same way we use chemical fertilizers would be pretty much the same in terms of runoff, disrupting balance, and causing algae blooms. It may leave a few living soil microorganisms in our fields though.