I dug into this a bit. A good metric by which to measure exciting (and very controversial) papers like the one referenced by that link is to see whether the papers have been replicated by others in well-regarded journals.

While the principal author of that article published an equally-controversial paper in 2005, follow-up studies suggest that there are no newly-generated egg cells in mammals [1]. I think it's fair to say, again, that stem cells don't play a role in maturation of adult egg cells.

http://www.ncbi.nlm.nih.gov/pubmed/23630252