Is that specifically the case? This feels like an area where our language can fail to capture the nuance of what someone is trying to say and it gets misstated as something really similar but different.
To give an example, take 3 people named A, B, and C. A and B are both from Africa, while C is from elsewhere.
A and B have 9 genetic differences. B and C have 1 genetic difference. A and C have 10 genetic differences.
We can make the claim that the genetic difference between someone from Africa and from elsewhere (B to C, thus 1) is much smaller than the difference between two people in Africa (A to B, thus 9). 1 is smaller than 9, so this statement is true, but could easily be misunderstood to saying that the two most genetically distinct individuals are from Africa, which isn't the case because A to C is the most genetically distinct and C is from elsewhere.
The two statements seem nearly equivalent and the wrong one could accidentally be spread by someone who is really just trying to focus on expressing how much genetic diversity is within Africa.
Africa is the continent on which humanity originated from, and peoples in other continents migrated in waves. So the most insular communities in Africa have had more time to diverge than the most insular communities in other continents.
They are talking with respect to internal diversity I believe.
As an Anglophone you may notice a similar thing in language, and in English you can notice the large diversity in accent in native UK speakers.
Non-Africans split from Africa relatively late in human genetic history. So A and B's divergence point(s) can readily be quite a bit earlier than C's. So, as you pointed out, C is likely more closely related one of A or B. Let's say B.
The big difference between B & C is that B is much more likely to incorporate genes from other early branches than C is. Therefore B is likely further away genetically from A than C is.
No, your split argument doesn't make the case you think it does. If groups A, B, and C were once groups A and B (and B split into B and C later), it's true that B and C are likely closely related, but it doesn't mean A and B are more different than A and C.
To put it another way, if we start with groups A and B, and then branch off B' from B, while B and B' are likely similar, that doesn't tell us anything about the relationship between A and B', and it doesn't imply that A and B' are closer than A and B.
I know that there is higher genetic diversity in Africa, and lower genetic diversity in non-African populations. That doesn't mean that there is greater difference between Africans and other Africans than between Africans and non-Africans; that only means there is greater difference between Africans and other Africans, than there is between non-Africans and other non-Africans.
To put it another way: there is extremely low genetic diversity in peregrine falcons; housecats have much higher diversity. But the two most-different individuals, when taken from a sample that contains both housecats and peregrine falcons, will certainly be a housecat and a peregrine falcon. Despite falcons having lower genetic diversity, they are still more-different from a housecat than any given housecat is from another.
Of course, humans are the same species, so it won't be as dramatic. But high genetic diversity amongst sub-Saharan African populations doesn't mean that sub-Saharan Africans are more different from each other than they are from East Asians (for example) — it only means they're more different from each other, than East Asians are from other East Asians. Pick any two people in China, and they're probably pretty genetically similar; pick any two people in sub-Saharan Africa, and they're probably pretty genetically different. That doesn't imply anything about how different the two Chinese people are from the two African people.
Additionally, non-sub-Saharan populations typically have some non-Homo-Sapiens ancestry: Neanderthal and Denisovan, for East Asians, and just Neanderthal, for Europeans. While genetic diversity within those groups is low, it doesn't mean that genetic distance from any given sub-Saharan group is low.
To expand the second part of my argument: If C' is only descended from C, but B' is descended from B and D and F and Z, then B' has increased its genetic diversity more than C' has.
To give an example, take 3 people named A, B, and C. A and B are both from Africa, while C is from elsewhere.
A and B have 9 genetic differences. B and C have 1 genetic difference. A and C have 10 genetic differences.
We can make the claim that the genetic difference between someone from Africa and from elsewhere (B to C, thus 1) is much smaller than the difference between two people in Africa (A to B, thus 9). 1 is smaller than 9, so this statement is true, but could easily be misunderstood to saying that the two most genetically distinct individuals are from Africa, which isn't the case because A to C is the most genetically distinct and C is from elsewhere.
The two statements seem nearly equivalent and the wrong one could accidentally be spread by someone who is really just trying to focus on expressing how much genetic diversity is within Africa.