From what I've read what happened is that a long time ago (hundreds of thousands, maybe millions of years) hominids left Africa, spread out and began diverging genetically. A short time ago (40-60,000?) a group of hominids in Africa left and spread out just like the previous wave of emigration.
I do not think the above is questioned by anyone. The debate is to what degree the 2nd wave interbred with the 1st wave. OoA theory says there was no interbreeding, which is convenient for multicult people as it "proves" that we are all similar. However, most evidence seems to point to at least some degree of interbreeding between the 1st and 2nd wave. Neanderthals were in Europe and the Mid East, so every race except blacks have some neanderthal in them. The group that settled a bit deeper into Asia has some of its genetic material in all the races that formed to the east of that point. Africans also interbred with archaic hominids, which is why they have genetic markers that do not occur in any of the races that left.
"Until recently, the out-of-Africa model of human evolution was favoured by most genetic analyses, but this model collapsed when the sequencing of the Neanderthal genome revealed that 1%–3% of the genome of Eurasians was of Neanderthal origin."
"The sequencing of another archaic hominin from the Denisova cave in the Altaï mountains in Siberia has further revealed that Papua New Guineans showed signs of introgression from this archaic human . Further studies of 33 populations from Southeast Asia and Oceania  showed that Denisovan admixture was actually present in other Oceanians, Melanesians, Polynesians, and east Indonesians but was virtually absent in mainland east Asians."
"In order to better assess the possibility of admixture in Africa, Hammer and colleagues  recently looked for signals of archaic admixture in two African hunter-gatherer populations and in a West African farmer population using a set of 61 non-coding autosomal loci. They found that an absence of admixture could not explain observed patterns of linkage disequilibrium in the hunter-gatherer populations, suggesting that they were potentially admixed with a yet unknown archaic hominin."
"There is thus both direct ,  and indirect ,  evidence for archaic admixture on four continents, suggesting that modern humans have not been totally genetically isolated since their emergence, some 150–200 Kya in East Africa , . However, there is still quite some discussion about the place, the timing, the exact numbers of admixture events, and the biological implications of these interbreeding events."
It is an interesting but academic argument. I don't care what people prove happened in the distant past, as it doesn't change the way things are in the present. Whether we diverged from blacks 50,000 or 50,000,000 years ago is irrelevant, as it doesn't change the degree of divergence which is easily evident without resorting to archaeology or gene sequencing.