"I've notice that many in broadcast media use both "African-American" and "black" within a single news segment or commentary piece, apparently in the effort to be as inoffensive as possible".

Both "African American" and "Black" are appropriate nowadays to refer to those people who used to be called Negroes. Imo, African American is more formal than Black. However, both can be used in ways that can be considered wrong-such as "The Black community" or the African American community. We are not a homogeneous group of people. For example, there are still Black folks [in the USA and elsewhere, too] who don't want to be called Black. And there are still African Americans that don't want to be called "African".

As to the term "Black" and "White" not being consistent with skin color, yes that's true.

Given the fact that for centuries persons who others consider to be {and who consider themselves to be} African Americans have ranged in skin complexion from lily white to blue black, and given not to mention the negative associations the color black has in Western societies, it's no surprise that Black was not selected as the formal group referent for African Americans.