We're trying to find out how much light comes out at a certain angle (represented by D). That depends on D(alpha), as the author states. However, it also depends on the intensity of light as a function of alpha. Much more light falls on the drop between alpha = 0 and alpha = 1 degree than falls on the drop between alpha = 89 degrees and alpha = 90 degrees. (In fact it's more than 100 times as much.)
This does not affect the final result of which angle is the rainbow angle. However, it does affect the distribution of light intensity as a function of D and the article is remiss to ignore it.