hmmmmm, the more I read about this fat thing the more I'm intrigued:
http://www.int-res.com/articles/meps/76/m076p295.pdf
I highly doubt corals can take up fatty acids directly from the water, the ones they get externally likely come from food. However, while some marine bacteria have the metabolic pathway to synthesize the polyunsaturated fatty acids (PUFAs) that most animals can't make on their own, I've found another study that showed bacteria are certainly capable of absorbing it directly from the environment if it's present, and that it will change the lipid profile of the bacteria when it does.
I'd be interested to see if adding milk to a tank alters the lipid profile of the bacteria the corals were feeding on, and in turn altered the lipid profile of the coral. Increasing the supply of certain essential fatty acids that the coral doesn't make on it's own, or doesn't get enough of from it's zooxanthella might encourage different concentrations/expressions of pigment proteins.
I suspect the 'dangerous' part relates to the gigantic supply of carbohydrate in milk, and the huge amount of carbon you'd be adding to the water in general. It would probably be pretty easy to OD and kill things.