This paper purports to affirm the genetic distinctiveness of Basques. However, they compare Basques with non-Iberians, so their claim only affirms their distinctiveness from non-Iberians, rather than their distinctiveness within Iberia itself.
So, I don't see any reason to doubt the findings of Laayouni et al. (2010) so far. If the authors of the current paper had carried out an analysis in which they included non-Basque Iberians, as well as geographically appropriate French (it is not clear how many HGDP French are from Basque-inhabited regions), then they would have a leg to stand on with respect to the alleged distinctiveness of Basques.
Moreover, their claim that their paper reaffirms Li et al. (2008) and refutes Laayouni et al. (2010) is similarly suspect, as Li et al. (2008) did not study Basques in the context of their Iberian neighbors.
What this paper shows is that French and Spanish Basques form a unit vis a vis other Europeans, but this does not justify the attack about the alleged shortfalls of Laayouni et al. In short it is difficult to see how to see how this paper's inflated claims have passed peer review.
Human Genetics doi:10.1007/s00439-010-0833-4
High-density SNP genotyping detects homogeneity of Spanish and French Basques, and confirms their genomic distinctiveness from other European populations
Naiara Rodríguez-Ezpeleta et al.
A recent study reported that Basques do not constitute a genetically distinct population, and that Basques from Spanish and French provinces do not show significant genetic similarity. These conclusions disagree with numerous previous studies, and are not consistent with the historical and linguistic evidence that supports the distinctiveness of Basques. In order to further investigate this controversy, we have genotyped 83 Spanish Basque individuals and used these data to infer population structure based on more than 60,000 single nucleotide polymorphisms of several European populations. Here, we present the first high-throughput analysis including Basques from Spanish and French provinces, and show that all Basques constitute a homogeneous group that can be clearly differentiated from other European populations.