I don't know if this question is too specific, but after reading Understanding Exposure, I can't understand very well the reasons and logic behind Brother Backlit Sky and their brothers. Although I did see that the pictures result more naturally pleasing.
I don't know if I can explain here what the book says as it's inside a paid book, but it has something to do with the metering system trying to convert everything to 18% gray.
From the book, you use Brother Backlit Sky when shooting backlit sunrise or sunset landscapes. Take a meter reading to the side of the sun and use it to make your image.