If you convert the red-orange scheme to grayscale you'll see that both the ugly and nice schemes have the same value contrast. If you convert the green-blue scheme to grayscale you'll see that the ugly combination has more value contrast.
See: http://img357.imageshack.us/img357/9127/grayfx0.png
The issue isn't contrast, it's hue.
The author uses the Müller Formula to explain it, but I'm not convinced about the "follow the natural brightness" argument – does that explanation still make sense if you reorder the colors in the scheme?
I learned this stuff in color theory without this formula. It's simply this: combinations of colors with similar hues don't look good together.
I hope this picture helps explain it: http://img181.imageshack.us/img181/3797/vomitev5.png
Obviously the left scheme doesn't look great in that graphic because all the colors have the same value. But you can see that it looks better than a scheme with colors of similar hue.