Ahhh.... I'm not entirely sure this is true, Ashkenazis don't plot in the Eastern Mediterranean between Cypriots and Mainland Greeks, I always plot in Southern Italy or in the Tyrrhenian Sea (west of mainland Italy). BTW, saying Ashkenazi Jews aren't European isn't entirely accurate either, Behar's recent study (2013) concluded that after Sephardi and North African Jews, Ashkenazis share closest genetic similarities with Mediterranean Europeans from Italy (Sicily, Abruzzo, Tuscany), Greece and Cyprus, Ashkenazis (and Sephardis) according to that study have something called K5, and if that K5 is removed then Ashkenazis shift from Italians and Greeks to the Druze and Samaritans, according to Behar's study that K5 presence in Ashkenazis and Sephardis suggests admixture with Non Jewish Europeans. Behar also concluded that Ashkenazi Jews derive their ancestry from Middle Eastern and European populations, so saying "Jews are Turkic steppe nomads" may be quite inaccurate, but saying "Jews are Europeans" isn't entirely inaccurate, genetically speaking and linguistically speaking, considering the fact that the Ashkenazi language is Yiddish, an Indo European High German language with it's main origin being in the Rhineland (being derived from old high German with minor Aramaic and Hebrew contributions). Here's the link of Behar's study, you may want to reexamine it.
Link:
http://digitalcommons.wayne.edu/cgi/viewcontent.cgi?article=1040&context=humbiol_preprints
Sicilians also plot in the Eastern Mediterranean, close to Cretan, Maltese and Aegean islanders (and of course, Ashkenazi Jews).
The main problem here is your assumption that "European" is a valid label in population genetics.
But for argument's sake, let's examine the claim... According to Lazaridis et al. 2013, Europeans derive from three ancestral population, Western Hunter-Gatherer (WHG), Early European Farmer (EEF) and Ancient North Eurasian (ANE).
These are real components, unlike Behar's K5 analysis, since the latter (like all modern-day components) derive from the the aforementionned components.
This is what the authors had to say about Ashkenazi Jews:
While our three-way mixture model fits the data for most European populations, two sets of populations are poor fits. First, Sicilians, Maltese and Ashkenazi Jews have EEF estimates beyond the 0-100% interval (SI13) and they cannot be jointly fit with other Europeans (SI12). These populations may have more Near Eastern ancestry than can be explained via EEF admixture (SI13), an inference that is also suggested by the fact that they fall in the gap between European and Near Eastern populations in the PCA of Fig. 1B.
And this is what the authors say in the sup data (revised version, 2014):
In Fig. S14.13 we present the range of parameter estimates. Some of these appear quite stable, achieving very similar values regardless of which individual population is fit, while others are less so, with the extreme being the amount of WHG ancestry in "Hunter", ranging from 0 to 95.7%. In that particular case, it was Ashkenazi Jews, Maltese and Sicilians for whom the value was 0, and Sardinians who had the highest 95.7% value.
[...]
Fig. S14.14 shows the range of values of x that were compatible with each population. While a wide range of values is consistent with each population, with the exception of some populations which are consistent with no WHG ancestry (Albanian, Ashkenazi_Jew, Greek, Maltese, Sicilian)
[...]
In Fig. S14.15 we show populations pairs that are consistent with descent from identical "Farmer" and "Hunter" populations. Sicilians, Ashkenazi Jews and Maltese are only compatible with each other and not with any other populations, consistent with Fig. S14.14 and Table S14.9 which show them to have less or even no WHG ancestry in contrast to other populations. Greeks are compatible with their geographical neighbors in the Balkans (Albanians and Bulgarians) and Italy (Bergamo and Tuscans). Basques andd Spanish_North are incompatible with several populations from Mediterranean and Southeastern Europe. Mediterranean and Southeastern Europeans such as Spanish, Albanians, Bulgarians, Bergamo, Tuscans, Croatians and Hungarians are compatible with each other
[...]
We repeated the joint fitting of population pairs, but allowed each population in a pair to descend from a different "Hunter" population, i.e, with a variable WHG/(WHG+ANE) ratio. Almost all population pairs were now successful (264 of 325, Fig. S14.17), with the exception of Ashkenazi Jews, Maltese and Sicilians who could often not be fit with other populations. It appears that these populations have Near Eastern ancestry that is not well-modeled by the 3-population model. This is consistent with their position in Fig.1B, and the results of analysis of SI 17 which do not explicitly model deep population history.
[...]
Three other populations produce anomalous estimates in Extended Data Table 2: Ashkenazi Jews, Sicilians, and Maltese. We observed in SI14 that these populations cannot be co-fit in the same admixture graph with most other Europeans, and this suggests that they do not fully trace their ancestry to the same EEF/WHG/ANE elements as most of Europe. Further evidence for this is presented in Extended Data Fig. 4 where all three populations have a negative value of f4(Test, Stuttgart; Loschbour, Chimp), and thus are inconsistent with them being populations of Stuttgart-related ancestry with additional Loschbour-related input, since such populations would have a zero or positive value of the statistic, as most Europeans do. All three populations strongly deviate towards the Near East in Extended Data Fig.4 and Fig. 1B, and it is likely that they possess Near Eastern ancestry that is not mediated via Stuttgart.
Ashkenazim basically show up as 93.1% EEF and 6.9% ANE
with no WHG.
Now you could argue that EEF is basically a mixture of Basal Eurasian with Near Eastern Mesolithic Hunter Gatherer components and some WHG, but if Ashkenazim truly were "Europeans" you'd also have to explain why they do not exhibit any WHG ancestry in such tests (remember, WHG is a true component, obtained from ancient DNA remains of European Hunter-Gatherers).
Last but not least.
The linguistic argument you put forth is self-defeating for two reasons:
1. Jewish languages merely reflect the host country where a given Jewish community emerged, if we were to follow your logic we could argue for instance that North African Jews (Moroccan and Algerian) are "arabs" or North Africans because they have their own Judeo-Arabic and Judeo-Berber dialects despite the fact that they're ~90% identical to the allegedly "European" Ashkenazim (since they speak Yiddish, which is IE), that they overlap on PCA plots and that they have high IBD sharing.
2. All Jewish languages were written with the Hebrew alphabet (Ktav Ashuri), the reason for this was their incapacity to transcribe typical Hebrew or Aramaic expressions (such as "Bli 3ayn haRa3", "HaShem Yiqom Damo", "Mazel Tov", etc) using the Latin alphabet.
So the theory according to which Ashkenazi Jews are francisca-wielding Franks who mixed with Judeans doesn't really work in my book... That's the least I can say!
And I'm sparing you painful details such as the paucity of "European" markers in Ashkenazi Jews (*cough* just have a look at your own uniparental markers for a start *cough*).
Now it's quite possible that Jews mixed with Europeans at some point, though the insane absence of WHG surely deals a huge blow to all the theories which portray Jews as "Near Eastern-European hybrids"... In fact, Berber ancestry in NA Jews is far easier to uncover than the alleged European ancestry of AJ (since they cline quite clearly towards NA populations).
The amount of admixture has yet to be assessed and accurately quantified, and the main problem here is that much of our current assessment is biased towards contemporary populations.
There's much to bet that the genetic landscape was quite different a thousand years ago, not to say two thousand years ago.
If I had to guess at this point, I'd say that most of the European admixture in Western Jews (Sephardic and Ashkenazi) was acquired during the early stages of the diaspora in the Eastern Mediterranean (which is why the picture we get is so blurry), think of the Kitos war for instance.
Behar et al 2013 does a fine job brushing Elhaik's funny theories aside, however it fails miserably in assessing the amount of admixture Jews were subjected to as well as the direction of gene-flow when using IBD segments.
In the end, the only way to truly quantify the amount of admixture is to obtain genome-wide studies of pre-exilic Judean samples... And even then, we'll still be splitting hairs when we get our hands on such a study (since Western Jews plot squarely in the Eastern Mediterranean).
Until this is done, I'd take every single claim of "European" ancestry with a few tons of salt if I were you, unless someone manages to explain the absence of the WHG component amongst Ashkenazim of course (which is easier said than done).
