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I think E-V13 people where paleo-balkanians who did not yet call themselves Greeks (Hellenes), Illyrians, Dardanians, Paeonians. Greeks and Albanians have the highest frequencies of this haplogroup, because they probably are the most related to these paleo-balkanic populations. Serbs, Montenegrins, Macedonian Slavs and Bulgarians, Bosniacs also share considerable Paleo-balkanic ancestry that's why they also have this haplogroup, albeit some perhaps in somewhat lower frequencies. Same can be said for haplogroup J2 which is mainly present among Greeks and Albanians but also in lower frequencies in South Slavs.
Which brings us to this Greek/non-Greek issue. Since most people in the Balkans (especially from the middle to the south)ever since pre-historic times shared the same bulk of ancestry, the term Greek or non-Greek was primarily based on culture. The geography of Greece, the sea, the islands, the trade routes, the warmer climate and the proximity to other civilizations helped the South-Balkanic peoples forge a unique culture and an identity which distinguished them from the more backward northerners at the time. Southern Greece became the core of this "hellenic" civilization and Epirus and Macedonia where considered by most to be the border line of the Greek world. While the area further north was barbarian territory.
Genetically though, there was little difference between the Greek world and the non-Greek world in adjecent areas. I.e. the genetic differences between Macedonia and non-Greek Paeonia would have probably been not much different compared to Macedonia and Thessaly or Epirus.
Based on this logic, it is very easy to assume why 'some' Southern Greeks may have considered border-line Greeks to be barbarians at some point in time while unanimously Greek at another time. One way or the other, racially they essentially belonged to the same stock. Even the ones who never come to belong to the Greek world because they were too far from the sea.