I think it's just a combination of hype, old wives' tales, and urban myths. Except...I know black skinned chickens are used in Chinese medicine, and maybe there is something in the pigment that has an effect. Or some other substance or combination of substances in that breed. I couldn't say. As an herbalist, I'm awestruck by the intricacy of Chinese herbalism, so far be it from me to dismiss black skinned birds as medicine. Chinese herbalists understand synergistic effects better than anyone else I've ever encountered.
As for plucking, I don't always manage to time the feathers right. Last fall I butchered some extra roos right after molt, there were the most gawd-awful pinfeathers, they took forever to pluck. These last ones were so easy to pluck, and came out cleaner than any I've done before, so know I know it can happen.
I've eaten plenty of birds with dark pigment spots, from feathers, in the skin. You can't taste it, and it's not noticeable after it's cooked. But people are funny, and they get grossed out about things that don't really matter. If you are selling your birds commercially, you may very well have customers who would freak out about pigment spots. The kind of gel-goo that's often present when you pull out a feather, is there on white feathered birds, too, but you don't notice it because it isn't black, like it is with a dark feathered bird.
I don't think there's any difference in flavor between a white skinned bird and a yellow one.
With milk cows, some breeds convert beta carotene to vitamin A better than others. They have whiter cream, because vitamin A is colorless. The others have a yellow tint to the cream, because beta carotene has color. The butter from that cream is a stronger yellow, as well. The same thing may be going on with different breeds of chicken, some convert the beta carotene, some do not. Those that do not, would have yellow skin.