I wish to point out that isn't the true Green color. If you had an (updated) model viewer, I could point it out to you. In the data files, there are 2 versions of each color -- there is the "real", which has the color tapers often to a white on the tips of the feathers (the blue and black on the left side show this nicely), and there are the painted colors. As you can see in
This link, you can buy a dye for your chocobo. The chocobo, when pained this way, often looks artificially colored -- the blue on the right side is a very good example of this, as does the red one. If you look closely on the red, in fact, you can see the tips, which would be another color, are pink. Regardless if you saw them or not, I am about 99% positive those are not natural colors, especially considering that there are exactly two of each color in the files (more, technically, which also detail the long beak, thick legs, and large feet, but the coloring is the same across those variations so they aren't considered).
I would also argue that, with all the effort that SE has put in to keep the game as reality-based as possible, at least when considering coloring and aesthetics, that there is no WAY they would put in such horribly colored chocobos that occur naturally.