It's interesting though, that Zhivotovsky is a co-author of this paper which states that:
A recent refinement of E1b1b1a-M78 by novel biallelic markers indicates that its subhaplogroup E1b1b1a2-V13 is the most common in Europe (Cruciani et al., 2007). In fact, E1b1b1a2-V13 originated in Western Asia about 11 KYA and expanded in Southeastern Europe about 4.5 KYA, not in connection with the spread of agriculture as traditionally assumed, but rather at the beginning of the Balkan Bronze age, as a consequence of the in situ population increase in the already populated territory (Cruciani et al., 2007).
and he was a co-author of King et al. (2008) which stated that:
The calculated expansion time of haplogroup E3b1a2-V13 in mainland Greece is 8,600 y BP at Nea Nikomedeia and 9,200 y BP at Lerna/Franchthi Cave and is consistent with the late Mesolithic/initial Neolithic horizon. These dates exceed those reported previously for Europe (Cruciani et al., 2007) that date to the Bronze Age. This discrepancy arises mainly because of differences in the choice of mutation rate used.
Peter Underhill was also a co-author of the latter study, and also of the recent paper on Sicily which used germline mutation rates and:
The estimate of Time to Most Recent Common Ancestor is about 2380 years before present, which broadly agrees with the archaeological traces of the Greek classic era.
Mesolithic - Early Bronze Age - classical Greek. Three completely different ages using three different mutation rates: a mutation rate 3.6x slower than the germline rate => Mesolithic. A mutation rate 2.4 to 2.8x slower => Early Bronze Age. A germline mutation rate => classical Greek.
My most recent take. I'll be much surprised if E-V13 turns out to be anything other than 2nd millennium BC in the Balkans.
American Journal of Physical Anthropology doi: 10.1002/ajpa.20933
Dissecting the molecular architecture and origin of Bayash Romani patrilineages: Genetic influences from South-Asia and the Balkans
Irena Martinovi Klari et al.
The Bayash are a branch of Romanian speaking Roma living dispersedly in Central, Eastern, and Southeastern Europe. To better understand the molecular architecture and origin of the Croatian Bayash paternal gene pool, 151 Bayash Y chromosomes were analyzed for 16 SNPs and 17 STRs and compared with European Romani and non-Romani majority populations from Europe, Turkey, and South Asia. Two main layers of Bayash paternal gene pool were identified: ancestral (Indian) and recent (European). The reduced diversity and expansion signals of H1a patrilineages imply descent from closely related paternal ancestors who could have settled in the Indian subcontinent, possibly as early as between the eighth and tenth centuries AD. The recent layer of the Bayash paternal pool is dominated by a specific subset of E1b1b1a lineages that are not found in the Balkan majority populations. At least two private mutational events occurred in the Bayash during their migrations from the southern Balkans toward Romania. Additional admixture, evident in the low frequencies of typical European haplogroups, J2, R1a, I1, R1b1b2, G, and I2a, took place primarily during the early Bayash settlement in the Balkans and the Romani bondage in Romania. Our results indicate two phenomena in the Bayash and analyzed Roma: a significant preservation of ancestral H1a haplotypes as a result of considerable, but variable level of endogamy and isolation and differential distribution of less frequent, but typical European lineages due to different patterns of the early demographic history in Europe marked by differential admixture and genetic drift.