I showed then not only that Elhaik's paper was sloppy and that the methodology was problematic, but also that Elhaik was clearly painting the bullseye after shooting the arrow - he intended from the beginning to prove the bizarre Khazar theory before gathering data, the exact opposite of how a scientist is supposed to act.
It turns out that the researchers who gathered the datasets that Elhaik cherry-picked to reach his foregone conclusions have demonstratively debunked Elhaik and his methods.
From their paper, named "No Evidence from Genome-Wide Data of a Khazar Origin for the Ashkenazi Jews":
Abstract. The origin and history of the Ashkenazi Jewish population have long been of great interest, and advances in high-throughput genetic analysis have recently provided a new approach for investigating these topics. We and others have argued on the basis of genome-wide data that the Ashkenazi Jewish population derives its ancestry from a combination of sources tracing to both Europe and the Middle East. It has been claimed, however, through a reanalysis of some of our data, that a large part of the ancestry of the Ashkenazi population originates with the Khazars, a Turkic-speaking group that lived to the north of the Caucasus region ~1,000 years ago. Because the Khazar population has left no obvious modern descendants that could enable a clear test for a contribution to Ashkenazi Jewish ancestry, the Khazar hypothesis has been difficult to examine using genetics. Furthermore, because only limited genetic data have been available from the Caucasus region, and because these data have been concentrated in populations that are genetically close to populations from the Middle East, the attribution of any signal of Ashkenazi-Caucasus genetic similarity to Khazar ancestry rather than shared ancestral Middle Eastern ancestry has been problematic. Here, through integration of genotypes on newly collected samples with data from several of our past studies, we have assembled the largest data set available to date for assessment of Ashkenazi Jewish genetic origins. This data set contains genome-wide single-nucleotide polymorphisms in 1,774 samples from 106 Jewish and non-Jewish populations that span the possible regions of potential Ashkenazi ancestry: Europe, the Middle East, and the region historically associated with the Khazar Khaganate. The data set includes 261 samples from 15 populations from the Caucasus region and the region directly to its north, samples that have not previously been included alongside Ashkenazi Jewish samples in genomic studies. Employing a variety of standard techniques for the analysis of population-genetic structure, we find that Ashkenazi Jews share the greatest genetic ancestry with other Jewish populations, and among non-Jewish populations, with groups from Europe and the Middle East. No particular similarity of Ashkenazi Jews with populations from the Caucasus is evident, particularly with the populations that most closely represent the Khazar region. Thus, analysis of Ashkenazi Jews together with a large sample from the region of the Khazar Khaganate corroborates the earlier results that Ashkenazi Jews derive their ancestry primarily from populations of the Middle East and Europe, that they possess considerable shared ancestry with other Jewish populations, and that there is no indication of a significant genetic contribution either from within or from north of the Caucasus region.
...One recent study (Elhaik, 2013), making use of part of our data set (Behar and others, 2010), focused specifically on the Khazar hypothesis, arguing that it has strong genetic support. This claim was built on a series of analyses similar to those performed in our original study that initially reported the data. However, the reanalysis relied on the provocative assumption that the Armenians and Georgians of the South Caucasus region could serve as appropriate proxies for Khazar descendants (Elhaik, 2013). This assumption is problematic for a number of reasons. First, because of the great variety of populations in the Caucasus region and the fact that no specific population in the region is known to represent Khazar descendants, evidence for ancestry among Caucasus populations need not reflect Khazar ancestry. Second, even if it were allowed that Caucasus affinities could represent Khazar ancestry, the use of the Armenians and Georgians as Khazar proxies is particularly poor, as they represent the southern part of the Caucasus region, while the Khazar Khaganate was centered in the North Caucasus and further to the north. Furthermore, among populations of the Caucasus, Armenians and Georgians are geographically the closest to the Middle East, and are therefore expected a priori to show the greatest genetic similarity to Middle Eastern populations. Indeed, a rather high similarity of South Caucasus populations to Middle Eastern groups was observed at the level of the whole genome in a recent study (Yunusbayev and others, 2012). Thus, any genetic similarity between Ashkenazi Jews and Armenians and Georgians might merely reflect a common shared Middle Eastern ancestry component, actually providing further support to a Middle Eastern origin of Ashkenazi Jews, rather than a hint for a Khazar origin.
The paper also publishes this graphic with this explanation:
Since this is a scientific paper, they can't say that Elhaik was a hack, but it is clear that his methods - using data from these very researchers - prove how low people will stoop to buttress their biases.
Figure 6 reports the mean genomic sharing between Ashkenazi Jews and the 11 population groups, and Supplemental Table 2 gives p-values for tests of the null hypotheses of equal mean IBD sharing with Ashkenazi Jews for pairs of population groups. The greatest level of sharing was observed with Sephardi Jews, considerably greater than with other populations. Substantial sharing with Eastern Europeans was also observed, though at a much lower level. Sharing with most other populations was lower still, and with Caucasus populations, the level of sharing was similar to that observed for the Middle East. In accordance with the results from other analyses, the IBD sharing of Caucasus populations with Ashkenazi Jews was relatively low.
Of course, the media will never give this study (written last year) the same coverage that Elhaik's lies received.
(h/t The Jewish Press)