First off, there are many definitions or concepts of what a species is. This classical article by Alan Templeton
http://www.omniscellula.net/simposi/articles/speciation.pdfprovides a review of some of them.
Now, as I see it, the statement that you cite is not referring to the typical definition that you mentioned (Ernst Mayr's "biological species concept", based on reproductive isolation). Rather, it is referring to the quantification of divergence of continuous characters between populations. These divergences are usually assessed either by morphological analyses, or by measurements of the differences in the structure of given molecules and macromolecules (proteins, histocompatibility complex, nuclear and mitochondrial DNA, etc).
BTW, here's another article on species definition that discusses a "genotypic cluster definition" of species:
http://abacus.gene.ucl.ac.uk/jim/pap/mallet95tree.pdfthat may be a good approximation to a genetic/molecular definition of species.
Molecular divergence can be measured, but the significance of these divergences is ultimately arbitrary, that is, the researchers decide, based on their calibrations of divergence between other populations, if the discrepancy is large enough that it can be interpreted as different species, or if there is enough internal molecular variability within those populations that the differences among them are not significant (as has been demonstrated for most of the variation among and within human populations).
See this example:
http://www.springerlink.com/content/4d9ku0ppcm6t0xjy/where the divergence between two populations was compared with other species pairs to decide if they should be considered as separate species.
As you probably know, sometimes (well, often) the results of morphological and molecular approaches do not agree with each other, because there are some major methodological differences, and the sources of data are quite different. However, combined approaches are (IMHO) what we the biologists should be working for.
Ultimately, I think these issues are consequences of our inbuilt need to put things into neat little boxes, that clashes with the infinite continuum of nature :-)