it's not saying that there at one point existed only one woman on earth who begat everyone

Right. What I was saying. She wasn't the only person ancestral to everyone or even the only female ancestral to everyone. But, as I understand it, she was the one whose daughters were the mothers of the daughters who were the mothers of the daughters... who were the mothers of everyone. Anyone else in there had males in their progeny who were part of the ancestry of everyone.