Actually AstroChuck, I think you were very smart to “seem to be exempt” because according to linguists they are not, even though it does seem that way.
I’m going to try to not explain every single concept in Linguistcs, but still try to answer your question (which can be difficult for me, so sorry if this runs a little long).
One thing first, an accent is one aspect of a dialect. I will refer to dialect from now on, keep in mind that this includes accent, and other factors such as vocabulary and syntax choices, and cadence of speach, among other factors.
Basically, you can think of language like a tree with many many branches. French, Italian, Spanish and Portugese are descended from Latin. English and German are descended from West Germanic. West Germanic and Latin are both descended form Indo-European.
Okay, so at some point in their infancy, Spanish and French were just dialects of Latin. They sounded a little different, but they were mutually intelligible.
So, today Southern accents and Northern accents are different dialects of English, just as African American Vernacular English (the linguistics name for African Americans’ dialect) is another dialect of English. EVERYONE HAS A DIALECT. In fact, no two people speak exactly the same way, and an individual’s unique way of speaking is called his/her idiolect.
Astrochuck, it sounds like you perceive the influence of AAVE more strongly than you perceive the influence of the geographic region in most African Americans’ idiolect. I think this is probably the case with a lot of people, but the geographic influences still exert and effect, it just may not be as pronounced. (As proof of this I can offer my linguistics teacher, who could tell all my classmates where we were from without asking us).
To answer your question, (up until now I was stating facts, but this part is hypothesis on my part) in America today, people move around pretty frequently, including black Americans. However, it is often the case that many African American develop social networks within the African American community, (churches, schools, neighborhoods) no matter what city or part of the country they live in, and so it is easier for you to perceive their sociolect (dialect based on social factors) than their regional dialect, but they do still have a regional dialect.