I think that sentence is misleading and is what caused the initial misconception.
Reducing the color palette is a technique for reducing file size. For example, say you have a grayscale image using 8 bits per pixel (256 colors). Ignoring other compression techniques, you can cut the size of the image in half by reducing it 4 bits per pixel (16 colors).
The naïve way to reduce bit depth is by discarding the low order bits, since they carry the least information. However, when you do that, the result is banding [1]. Banding is an unsightly artifact.
Dithering exists essentially to deal with banding. It works by (sort of) adding a slight amount of noise to the pixel values to diffuse the transitions between diffferent thresholds.
But anyone with an ounce of information theory will tell you that noise by definition is literally the hardest thing to compress. So when you dither an image, you are throwing away almost all of the gains you got by reducing the bit depth in the first place.
