(1) Genetic differences between Northern and Southern Europeans are of little importance.
(2) The existence of substructure within Northern Europe is of great significance.
I'm sure Rienzi will insist that's not what he wrote. But his thought process seems clear. (Or, alternatively, Rienzi would prefer to ignore genetic differences within Europe entirely, but believes he can play "gotcha" with those who would distinguish between N. and S. Euros by pointing out variation among N. Euros; Rienzi has openly admitted as much this in the past.) Needless to say, this sort of logic doesn't work.
Rienzi acknowledges "the major genetic clustering in Europe is along the North/South axis", but doesn't seem to grasp how "major" this axis is. To put some numbers on it, in Tian et al. (2008) PC1--the "North-South" PC--explains 42.42% of the total variance in the first 10 PCs. The next largest PC takes in 8.32% of the variance, with the remaining PCs each being responsible for less than 7%.
The historic/Neolithic/Paleolithic debate is a red herring. The question is simple: how closely are various populations related today. And what do the numbers say? Southern Europeans are more similar to Ashkenazi Jews than to the Northern Europeans. From Price et al. (2008):
We computed FST statistics between clusters 1 (mostly NW), 2 (mostly SE) and 3 (mostly AJ), restricting our analysis to individuals unambiguously located in the center of each cluster (Figure 2). We obtained FST(1,2) = 0.005, FST(2,3) = 0.004 and FST(1,3) = 0.009.
No one has ever argued the above indicates Southern Europeans "are Jews"--though, in terms of genetic distance, Southern Italians and Greeks are over half-way there.