How are you defining a "white" person? Simply as someone who manifests with white skin (notwithstanding albinoism)?The off spring of black people are black at birth and the off spring of white people are white at birth.
If, for example, you have white skin - and even all the other physical characteristics of a "white" person - but are yourself of mixed black/white parentage, you could marry a white person but still give birth to a black child. It's all about the genes, and which are dominant in the child. And the dominancy of some genes might skip a generation.
It's not common, for sure, but it is possible. Your quoted comment above is a reasonable rule of thumb, I think, but not absolute.