I have to disagree. Zooxanthellae is brown. The colors come from Chromoproteins/Photopigments NOT the Zooxanthellae. By simply reducing the amount of nutrients thus reducing the density of Zooxanthellae the corals will lighten up but not necessarily "color up". You see this all the time with sterile barebottom tanks. The nutrients are low but the corals look light and faded.
Some corals have the ability to create these desired chromoproteins/photopigments when proper conditions are met and some not so much. Which is why there are some corals that stay colored up much easier and some which always remain "blah".
If the needs of the coral are met, lighting , food, flow etc in conjunction with low nutrients (reduction in Zooxanthellae) then one can get corals to achieve these vibrant colors. Obviously this is what we all try to achieve. The corals lighten we feed more. Then we feed too much and phosphate leves rise and they start to brown. So the best of both worlds would be to have good nutrient export while still supplying adequate amount of food at same time. This is difficult in a closed system which is why methods like Zeovit, Prodibio, GFO, Refugiums, Powerful Skimmers all play important roles.
Some reading if you are interested:
http://www.advancedaquarist.com/2006/9/aafeature/view