i had to write on this question for as part of my master's qualifying exams in 1995, when it was a fairly new issue.
fact is, to the best we (anthropologists) know it, we did descend from a common african ancestor.
the question is timing. the "eve" folks say 200,000 years ago. the fossil record (i.e. actual human remains) differs. probably happened about 1 million years ago, give or take, according to it.
the sinodont (typically chinese dental pattern with shovel-shaped incisors) has existed for 1.5 million years. still there. no african teeth in china. the large browridge of australian aboriginals also well predates eve, and is still around.
the eve hypothesis rests on some pretty shaky logic. they based the 200k years on the amount of change found in mitochondrial DNA per the rate of change found between humans and apes. they assumed a linearity of change, and that the human-chimp split date was accurate. this goes to the gradualism notion of evolution, which has been replaced by a punctuated equilibrium theory, so assuming linearity is kinda, uh, dumb.
the argument rests also on the absolute extinction of all other maternal lines. i.e. the ancestors of eve must have a survivability advantage that they survived when all other lines became extint. as i wrote seven years ago "eve's kids must have been very smart to hide in caves while every other humanoid on the planet was killed by the alien death rays." yeah....
i also threw in some shit about population genetics that i don't remember, but it was a convincing argument to my examiners. suffice to say, eve didn;t stand up well to the argument.
the eve hypothesists were a bunch of folks from UC berkely if i remember correctly, probably trying to capitalize on some notion of "race harmony" by suggesting such a recent split. not that i have a problem with race harmony, all for it, but their ideological biases became obvious with the briefest examination.