You're right, it needs both. In fact, in the presence of strong light, algea will try to grow even if phospates are relatively low. That's a big reason water quality is so important in this hobby. Most of us shine a ton of light into our tanks for the sake of our corals, so since we can't get rid of the light, we have to try and get rid of the chemicals.
_________________ Mercedes W125
somewhat, however nutrient export is the most important factor. GFO media (phosban, rowaphos, etc) is IMO, the best tool we have against algae control.