Actually, I'm not sure that's true. There's hardly any UV in tanks, and there are plenty example of very successful and colorful acro tanks out there with only PC lighting...
Sometimes... there are numerous pigment types in the coral skeleton that are partially responsible for coloration. There are various reasons these pigments can change. Everything from predatory response, diet (vitamin intake), etc.
Zooxanthellea inside the coral change pigments primarily in reaction to light intensity including UV light.