Although I can't prove it, I believe small to be quite accurate!!
To explain is difficult, but I think that there are so many factors affecting color, that lighting becomes a small part. What type of fish you have and what the eat dictate, to a degree, what food is available for the corals. This fish excretment contains varying amino acids, organic and nitrogenous compounds. These "ingredients" will play a role in the production of pigment proteins within the coral tissue. This will be similar to dissolved organics in the water column also.
I have witnessed alkalinity affect coloration also. When I bumped my alk up from high 2s, to mid 4s, I noticed a color shift in many corals. I confirmed this with other hobbyists.
I believe flow can affect coloration, as can temperature. Reaction rates within the tissue will be dependant on temp(and enzymes, etc...negligble for our purpose).
I believe lighting intensity (wattage and/or proximity of bulb) as well as duration of the light energy will affect the coral, but I don't feel color temp has a big impact.
Unfortunately you'll find as many "experts" that agree with this as don't.
Like I said, I can't prove it scientifically, but my observations are common among many others in the hobby.