As a white person, I don't have to worry about my skin tone being too white; about being perceived by others, including my own race or ethnicity, as being somehow less than for having a lighter complexion.
But as the (beautiful) Black women in the video explain, there is a stigma to having dark skin, even within the Black community. Our society - Black and white - (still) objectifies and dehumanises people with dark skin. As the little girl demonstrates, dark skin is associated with stupidity and ugliness, even from an early age.
A friend of mine was telling me yesterday that her 8-year-old niece, who is black, insisted on having a white, blond-haired doll rather than a dark-skinned doll. I can only imagine the psychological factors that go into such a choice, but I suspect that little white girls would likely play with white dolls as well, dolls that actually look like them. They wouldn't be compelled toward the other. I wonder whether this is because for Black people, the other is constantly portrayed by society, and especially popular media, as the better.
As a fair-skinned person, I don't have this problem. I'm constantly told - even if subliminally - that I'm the better. More beautiful, acceptable, lovable.
Just another tool for my knapsack.