I just whipped up a case study. I added some white stripes to the wings of a 109G-6 scheme that already had white parts. All white areas on other part of the main scheme are darkened with 15% black. The stripes are a combination of a 100% white portion next to a darkened portion, 15% black on the left wing and 20% on the right. The stripes have the same specularity as the camo paint to really illustrate how the white reacts.
First pic. Shows the difference in the strait white and the faded white

Second pic: Focal point is washed out to the same level, but the radius of the washout is reduced with faded whites.

To my eye, 20% black turns the white too gray in normal lighting.