What corals don't need food
The confusion is that everyone is right...almost. First, all photosynthetic corals can exist on light alone, but that process just produces sugars. As you would guess, a steady diet of sugar isn't necessarily a good thing, so they also feed using their polyps. You can accelerate the production of polyps and overall growth by having some food available in the water flow. If you have fish, that's probably enough floating nutrients all by itself. But corals do respond well to occasional feeding. I don't use the bottled phytoplankton but I do use a bit of Reef Chili squirted at night on each coral weekly.
Hope that helps some.