Can African Ancestry really tell which African country an African American's ancestry is from?

Probably not. Keep in mind Africa’s political instability. Those countries may be long gone.

There was a lot of movement then. Some tribes captured others and sold them into slavery. Who knows how many captive women were raped by men not of their own people before being sold to Europeans?

The point of origin [slave records] may not match the true tribal area. Some tribes may have been eradicated completely through tribal wars. Sierra Leone Ivory Coast, Ghana and Nigeria were centers for the Portuguese slave trade to buy from African traders. Benin was a rich nation in the area then known to Europeans as Negroland.

The eastern or Arab slave trade was handled out of what was then called “Nubia”.
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In this USAToday article, about 30% of African-Americans who had DNA testing showed European ancestry through their father, and close to 100% show African heritage through their mother.

It depends on the haplogroups, see

http://en.wikipedia.org/wiki/Mitochondrial_Eve

http://en.wikipedia.org/wiki/Human_Y-chromosome_DNA_haplogroup

http://en.wikipedia.org/wiki/Haplogroup_L1_(mtDNA)#Tree

So if an African American belongs to L1b1a3a1 for example the location of origin can be determined with greater precision.

If it says the DNA match is Nigerian, what that means is that there is a DNA match to one of the 250+ different ethnicities of Nigeria. (How do I know this? I’m Nigerian).

Now even though Nigeria’s population is so diverse, only a few of our ethnicities are nomadic. (Fulani primarily).

Controlling for location, an African American whose DNA shows a match located in Nigeria is almost 90% more likely to have a match in Southern Nigeria as opposed to Northern Nigeria (this is because the slave trade / most of the slaves that were captured and transported to the United States and other places came from Southern Nigeria ).

In other words, the chances of an African American having a DNA match to Hausa ethnicity (which is the largest ethnic group in Northern Nigeria) is less than 10%.

Conversely, the chances of an African American having a DNA match to Igbo, Yoruba, Bini, Efik, Igala, Ibibio, Ijaw or Itsekiri ethnicity (assuming they have already been DNA matched to Nigeria in general) is almost 90%.

When you then factor in the fact that Igbo and Yoruba account for the vast majority of all the people in Southern Nigeria, an African American who has been DNA matched to Nigeria in general has an extremely high chance of being either Igbo or Yoruba and a moderately high chance of being from one of the other southern ethnic groups.

So there you go.