It's a simple and attractive story, but one which is wholly dependent on ignoring admixture. There are two types of admixture that are pertinent: one is admixture between modern human groups. An example of this is Ethiopia. Many studies have presumed to identify a signal of Out-of-East Africa based on diminishing distance from East Africa. But it is completely unclear how this model fares when one takes into account that East Africans are a recently admixed population: their great genetic diversity may be due to the recent intermingling of two very divergent groups of people (Caucasoids and aboriginal East Africans).
Or, consider two Englishmen, one with a Nigerian and another with a Chinese grandparent. These two individuals might appear greatly diverged from each other genetically and phenotypically, but this is the aggregate of sharing 3/4 of quite recent common ancestry (from their English grandparents), and not sharing 1/4 each of highly divergent ancestry (from their Chinese and Nigerian ones).
The situation is more interesting when we realize that admixture can occur not only between modern human groups, but also between modern humans and archaic ones. Both archaic genomes published so far (Neandertal and Denisova) show differential affiliation to modern human groups, and indirect evidence suggests that some African groups also admixed with archaic species that once lived in Africa.
Of course, levels of archaic admixture inferred from these studies are usually small, but we must remember that a little archaic goes a long way. This is due to the fact that modern humans and archaic ones diverged from each other a long time ago. Their admixture, even in highly favorable (for modern humans) proportions introduces a substantial amount of new genetic variation. As a result, populations harboring archaic admixture appear more divergent from each other.
This point is made quite well in a new article:
If human populations do not all have the same level of archaic introgression, the current genetic structure of human populations might be partly shaped by differential admixture. Estimates of population sizes and divergence times between human populations should thus be affected by past admixture events. The divergence time between an admixed and a non-admixed population should be overestimated if admixture is not properly modelled. Similarly, the effective size of admixed populations should be overestimated as archaic lineages inflate genetic diversity. In Figure 2, we report a simulation study of this bias in a very simple case of population divergence without migration. The overestimations of divergence time and admixed population size are almost linearly increasing with admixture rate (Figure 2). For instance, a divergence time of 1,600 generations (40,000 y assuming a 25-y generation time) is perfectly recovered if none of the populations is admixed, but is overestimated by 100 generations (2,500 y) with 1% admixture in one population, and already by 350 generations (8,750 y) with 5% admixture. Even though our simulated scenario is unrealistically simple, it is likely that differential admixture should affect population genetic affinities under more complex models of population differentiation. The proper interpretation of human genetic affinities should thus probably be re-evaluated in the light of these results. In particular, the divergence between Africans and Oceanians (showing up to 5% archaic admixture ) could be more recent than previously reported (62–75 Kya ). It remains unclear whether the method used by Rasmussen et al.  to date this divergence is also sensitive to differential introgression, but, if that was the case, the colonization wave to Oceania thought to well predate that towards East Asia  could have occurred at roughly the same time once differential admixture had been taken into account.This is an important point: the inferred early dispersal of Oceanians could in fact be the result of archaic admixture in both Africans and Oceanians.
Lower levels of archaic admixture are sufficient to make two individuals or populations appear much more distant from each other. Archaic Homo populations may be as much as an order of magnitude more divergent to H. sapiens that particular H. sapiens groups are to each other.
But, admixture can also deflate divergence, if there is subsequent gene flow between the diverged populations. As an example, Near Eastern Arab populations: have both diverged from Europeans due to receiving African admixture, and also converged with them by the fact that Europeans have Neolithic Near Eastern admixture which renewed bonds between Europe and the Near East. It means little to speak of "when" Europeans and Near Eastern people diverged from each other: it's a balancing act of centrifugal and centripetal influences: if a Crusader lands on the Levant and marries a local woman, he diminishes apparent Europe-Near East genetic divergence; if a Somali does the same, he increases it. So, in the end, the apparent "divergence" between Europe and the Near East may have little to do with how much time has transpired since the colonization of a new region, and more to do with "who had sex with whom" in the intervening period.
In fact, the ability of admixture to "converge" populations is the basis of the multi-regional evolution theory, although that is usually posited in terms of gene flow. But, the basic idea is still the same: our relatively uniform human species may not be entirely the result of tree-like divergence of populations from an original African population, but rather of a confluence of streams of ancestry derived from Lower and Middle Paleolithic populations of Homo.
Admixture may not only lead us to overestimate divergence between populations: it might lead us to wrongly estimate the directionality of migration itself.
Consider a future geneticist, working thousands of years after a collapse of civilization in the near future which led into a breakdown of long-distance travel. Such a scientist would perhaps conclude that the highest genetic diversity is to be found in North America, and conclude that North America colonized the rest of the world.
In some cases, it can well be argued that serial founder effects/bottlenecks restrict genetic variation/effective size. For example, the colonization of the Americas in three waves created a population that is clearly a subset of the East Eurasian parental population. But, notice that researchers trying to understand it had to carefully disentangle the various migration waves and cleanse their data from recent European admixture. The directionality of migration can be recovered through a diligent treatment of the evidence.
But, let's forget about the nested-subset analogy: the fact that a population X may appear to be a subset of another Y does not indicate that Y founded X any more than the fact that the genetic variation of any single European country is a subset of the cosmopolitan populations of the Americas will indicate an America-to-Europe migration to the future geneticist. Sometimes, X is a subset of Y because Y has a superset of variation formed by union with a divergent other population.
Sub-Saharan Africa is one example of a terra incognita for the historian. In the absence of written sources, science is mostly clueless as to what was going on there for thousands of years after the invention of writing in Mesopotamia. In some areas, due to the moist climate/abundant vegetation/political instability even archaeological evidence is lacking. What this means is that we are in the dark about what admixtures were going in the Dark Continent. Thankfully, people are working on it.
My own position is that while an origin of anatomically modern humans in Africa still seems to be correct, the pattern of divergence and reduced effective size of Eurasians from Africans is not wholly due to a small group of them leaving the continent at some Middle Pleistocene epoch.
How much of the African divergence and higher African effective population size is due to a Biblical-level bottlenecks coinciding with Out-of-Africa? As readers of the blog know, I don't buy the recent Out-of-Africa model, especially in its "endangered but crafty tribe of pioneers following the coast 60,000 years ago" variety. Archaic admixtures in Eurasia and Africa inflate divergence times; back-migration may deflate them. It's yet another balancing act.
Hopefully statisticians, with a little help from archaeology and palaeoanthropology can untangle the palimpsest of events and present us with a believable story about our own origins. It's time to give up trees and embrace networks!
PLoS Genet 8(7): e1002837. doi:10.1371/journal.pgen.1002837
Genomic Data Reveal a Complex Making of Humans
Isabel Alves et al.
In the last few years, two paradigms underlying human evolution have crumbled. Modern humans have not totally replaced previous hominins without any admixture, and the expected signatures of adaptations to new environments are surprisingly lacking at the genomic level. Here we review current evidence about archaic admixture and lack of strong selective sweeps in humans. We underline the need to properly model differential admixture in various populations to correctly reconstruct past demography. We also stress the importance of taking into account the spatial dimension of human evolution, which proceeded by a series of range expansions that could have promoted both the introgression of archaic genes and background selection.