Well, it's not that simple, really. But cultural forces inside and outside the LDS church have sort of forced things into these polarizations.
The truth about the racial mix of human populations in reality is quite difficult to divide into two "racial" camps. Tribes and entire peoples intermarry and racial distinctions become hard to distinguish. Ultimately, we're just talking about one race...the human race...and nothing else about them really matters beyond that.
But if we're going to insist on going down this road of "who was white and who was not", we might as well start with a new DNA discovery that portrays the origins of at least some groups of original inhabitants of the American continents as distinctly white.
What scientists found predates even the earliest estimates of the arrival of the Jaredites (the first Book of Mormon people, even if their story appears at the end).
About 11,500 years ago, just as the last ice age was drawing to a close, a woman gave birth in an Alaskan valley to a child who didn't live very long. She buried the remains next to another likely stillborn child (perhaps a cousin) in a burial pit. Those remains, discovered in 2013, hadn't been able to be fully analyzed until very recently.
Expecting the first child's DNA to come closer to matching modern Native American lineages, they discovered that the genetic markers pointed to a completely different origin.
Named the "ancient Beringians", this group seems to have come from European groups nearly 20,000 years ago. They had come to Alaska over a frozen land bridge from Europe and Asia and then continued south, likely in a single wave.
Please know that by posting this I'm NOT jumping onto any bandwagons about which races might be superior or pure or chosen or "first" or any of that other nonsense. No way. I'm just interested in the science of migrating people and how that might have looked before, in, and after Book of Mormon times without regard to anyone's preconceived notions about whiteness, brownness, or blackness.
That is all.
Find out more about this fascinating research at http://www.pnas.org/content/111/48/17060.full.