Part of what makes lots of games enjoyable is a certain degree of fantasy, even in more "realistic" games like the COD series. There's also a significant difference between the feeling of being told a story through the campaign and the feeling of making a name for yourself in PvP.

I think the developers made the right choice here; the story they tell is "historically accurate" in that the uniforms and decorum for each side is accurate (though the events I'm sure are false). In PvP, where players typically are just interested in having a good time, it makes sense that nobody is forced to be on the side of history near-unanimously regarded as evil and worse. It's just side A vs side B. Moreover, PvP is where many players like to customize their character, so I'm sure all the black female gamers out there are appreciative that they can finally see something on the screen that looks like them.