I, also haven't read the orginal paper but I think that I understand roughly what was done.
I think they have shown that an individual in the not too distant past
could have been a common ancestor to all of us. That does
not say that is what did happen.
The model is then tested against real evidence and, as RASD notes, seems to be found wanting.
I'm not sure how this model could conclude that even if one person could be an ancestor that, in fact, many people were also common ancestors to us all.
I recall from the radio about a decade ago someone modeling populations who concludes that anyone born in Britain would, going back about 600 years, be related to about 80% of todays population. IIRC his model also concluded that going back further did very little to that 80%. There are always people around with whom you do not share ancestors in his model.
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