True, but even Joe Louis would not have been able to lead very many soldiers into battle; the military was segregated until at least 1948, and less than 10% of the soldiers in the entire war were black (not sure, precisely, how it falls, Europe vs Asia).
So they fudge the rules because they've got a Super Soldier who's black. They can address that, even. Steve Rogers was the best candidate, and they "make do."
Military Scientist: He's the best candidate, period.
Joint Chief: Hmm...really?
Military Scientist: Yessir.
Joint Chief: Then do it.
Lower-ranking Official: But sir, he won't be able to lead white soldiers!
Joint Chief: Blast the rules! Do it, Dr. Military Scientist Guy!
Or they could just have him be a one-man unit.