There are other reasons that colorful corals could have a lower electron transport rate (as demonstrated by various researchers).
Fabricius showed that colorful corals retain less heat than colorful ones. Does this play any role at all? No one to my knowledge has connected the dots on this one.
The zooxanthella clade could play a difference - some adjust to light intensity by adjusting their numbers, some adjust the PSU size. Some are heat or bleaching resistant due to the chemical compostion of the thyllakoid membranes. Color might have nothing to do with their photosynthetic capacity.
Sure, I would never argue that we are at all certain about what these proteins do or how exactly they do it.
A friend was meaning to work on the effects of colony pigmentation on sensitivity of the zoox. to temperature stress, but I'm not sure how much she's been able to get done with that. Darker or more colorful colonies do tend to be warmer than lighter or unpigmented colonies, and that microtemperature could exert selective pressure against those colored corals during high temperature stress, as suggested by work from Fabricius et al.
The bulk of my friend's work deals with looking at differences in susceptibility to temp stress and connecting that to differences in thylakoid membrane composition (and hence fluidity).
Generally zoox. make adjustments for differences in light intensity by changing PSU size and pigment density, but not by changing their density within the coral. That would increase shading on each zooxanthella--how could that be used as a mechanism to reduce light limitation? Besides, many studies have shown that zoox. density is similar over a range of depths in a given coral.
But having said all of this, I still don't see any reason that we should think light spectrum incident on the corals should affect the production of pigments that we agree may or may not have anything to do with the fact that they interact with light.
Smarty pants ;-). The point is that spectrum is often an important part of photochemical responses. I don't have time to pick through the references, so I'll cut-and-paste a partial list - there are some real gems buried in the biomedical literature!
Ha,

Yes, spectrum can play a part in biochemical responses, but only when spectrum is an important factor in the functioning of these processes.
For example, there's no reason that insulin production in our body should be affected by the color our eyes see. There would be no benefit to doing so. On the other hand, there IS benefit to detecting increases in UVR and UVR damage. Thus, when exposed to increased UVR, we tan.
I'll take a look through that lit. list when I get a chance.
Chris