Many indians are as dark skinned and would probably have the same problem. Do you also refer to them as "black people"?
In the U.S, "black" is a race, it's not a skin color. About 70% of "black" people in movies and music have light skin color that would probably not have the same camera problem.
So technically, saying "black people" would be wrong. The technically correct term in this particular example would be "dark skinned people".
It's something of a generational thing. I'm overgeneralizing, but self-identifying as black is more common in Generations X and Y and self-identifying as African-American is more common among Baby Boomers.
Please, don't be PC when there is no reason to. This is one moment that it is more correct to say "black people" than anything else.