1. Imagine a conceptual sunbeam originating from the sun and passing through the sky high over your head.
2. This sunbeams low-frequency components ("reds") continue on in their straight path, making them invisible to you.
3. The high-frequency components ("blues") are scattered by the atmosphere, going in random directions. When you look at the sunbeam, you can see these scattered blues, making the sky blue.
4. A cloud floating up in the atmosphere is illuminated by some direct sunbeams, which are "red".
5. It's also illuminated by the scatter from the atmosphere, which is "blue".
6. Do those two sources balance out exactly such that the light exiting the cloud has the same profile as light exiting the sun?
If you look at the solar radiation spectrum chart in the section "Why isn’t the sky violet?", you can see that sunlight is not evenly distributed along the visible spectrum--it emit more blue than red, and at sea level it's closer to evenly distributed. So the light that reaches the clouds is still mostly white light.
I think it may also relate to chromatic adaptation. To be white it doesn't need to be any exact absolute color just the color our brain sets our white point to.
Not answering this question but I found an interesting short paper about how at sunset and sunrise the color gamut of shadows doesn't fully overlap with the direct illumination color gamut due to the differences in the paths the light takes:
Hubel. 2000. The Perception of Color at Dawn and Dusk.
1. Imagine a conceptual sunbeam originating from the sun and passing through the sky high over your head.
2. This sunbeams low-frequency components ("reds") continue on in their straight path, making them invisible to you.
3. The high-frequency components ("blues") are scattered by the atmosphere, going in random directions. When you look at the sunbeam, you can see these scattered blues, making the sky blue.
4. A cloud floating up in the atmosphere is illuminated by some direct sunbeams, which are "red".
5. It's also illuminated by the scatter from the atmosphere, which is "blue".
6. Do those two sources balance out exactly such that the light exiting the cloud has the same profile as light exiting the sun?