As this result shows, we don’t have to come up with an explanation like President Obama’s—it doesn’t have to be that her mom was Caucasian. Because of how these tests work, the DNA from this test could have come from a woman five, ten or even fifty generations back. Mitochondrial DNA passes from mother to child virtually unchanged, generation after generation.
What this means is that there is no dilution of mtDNA as the generations pass. Mom’s mtDNA is pretty much the same as grandma’s which is pretty much the same as great grandma’s and so on. This DNA doesn’t dilute over time.
Here is one way to show what might have happened to this woman’s DNA over the generations:

In the diagram, circles are women and squares are men. Also, white means Caucasian and black means African.
On the left, we are following the mtDNA of the tested woman and on the right we are following the rest of her DNA. She is the circle at the bottom of the family tree on each side.
What you can see on the right is that over the generations, the original Caucasian DNA is being diluted out. It goes from 50% to 25% to 12.5% and so on as you’d expect. The same isn’t true for the mtDNA on the left. It stays Caucasian generation after generation.
So if we look at most of her DNA, she looks African-American. We may not even see that sliver of Caucasian! But her mtDNA is 100% Caucasian. No wonder she was confused.
Obviously she can’t find out what part of Africa her ancestors came from with this test. But let’s say she got a more typical result and her mtDNA could be traced back to some part of Africa. What does that result really mean?
As the result here shows, it may not mean as much as she hopes. Imagine the previous scenario but instead of being Caucasian, the woman from five or ten generations ago came from a different part of Africa than the rest of her relatives. She would come away thinking her relatives were from one part of Africa when most of them were really from another.
She would not get the answer she was looking for but there is no way for her to know she got the “wrong” answer. She would simply go on believing she was from a part of Africa she really wasn’t.
Unfortunately, there really isn’t a better DNA test for looking back in time. The most useful tests, the autosomal ones that look at all our DNA, can only go back four or five generations before becoming hopelessly jumbled. For most African-Americans, this isn’t far enough back to find their African ancestors.
The other kind of test, the Y chromosome test, can go as far back along the paternal line as the mtDNA test can along the maternal line but it suffers from the same problems. In fact, a surprising number (35%?) of African-American men actually have Caucasian Y chromosomes (well, given plantation life, maybe not so surprising). None of these men will learn anything about their African heritage with this test.
So the bottom line is don’t put too much faith into DNA testing alone. It is kind of fun to trace back your history this way but you are really only following one strand of your ancestral web back in time. The rest of the web is invisible to DNA testing.
Of course mtDNA tests have been incredibly useful scientifically. They’ve let us trace human migration as we spread out of Africa and even trace all of our lines back to a single woman, Mitochondrial Eve. Recently these tests were even used to confirm that a skeleton found under a parking garage in England belonged to King Richard III.
Just don’t count on mtDNA tests giving you a broad understanding of your own family history. They won’t.