I asked my dad about this once and he said it's possible for this to happen without anyone cheating. Many black people were breeded back in slavery times so their kids were white as hell. It's possible that after slavery, these white looking blacks didn't realize they had black blood in them and kept mating with whites. Upon chance, the black side could surface and be darker than the mother or father.
Many black female slaves were raped by their white masters. That's why there were many children who looked white. They looked white, because they were partly white. The average African American (self reported) has 20% European ancestry and according to genetic studies, most of that isn't recent.
As far as I know, the genes that code for skin color are additive. So if someone carried genes that coded for black skin color, you'd likely see it. Though, if one parent carried one gene that coded for black skin color and another carried one gene that coded for black skin color they could pass both genes to the child and he or she would have darker skin than either parent. Or they could pass none of the genes and the child could have lighter skin.
Your father is correct, many black people did pass off as white (well technically they were mostly white) and they did marry other whites. That's why the average white person (self-reported) has 2% African ancestry (that's not to say every single white American has 2% African ancestry, as two-thirds have none and others have significantly more ).
*Numbers are off the top of my head.
**did not watch the youtube video (Firefox issues).
