You dont see this question asked a lot in a modern context because modern historians do not touch topics like this. The reason they dont is because its a nationalistic question, not just for Greece but for all those nationalist groups in other countries that dont like Greece or Greeks. These are the kinds of questions that were popular during the days of racist ideologies like the "white man's burden". Ill give you some sources to look at though.

Anyway there were people in Greece from places like Scythia, Thrace etc. even before 400 B.C. so there always has been intermixing. There is no such thing as a "pure race' and the whole idea of "racial purity" is racist rhetoric that isnt true for any group and there are plenty of other theories like it, such as for nations like Japan and their Korean/Chinese influence etc.

http://onlinelibrary.wiley.com/doi/10.1002/oa.2459/abstract

King Phillip II buried with a Scythian Princess

The "Greek theory" emerged because of the racist ideologies in the early 1800's and the events that unfolded after the congress of Vienna. The congress of Vienna advocated for keeping the balance of power in Europe and preventing the rise of revolution because of what happened during the Napoleonic wars. Then the Greeks looked to gain their independence and the creators of this keeping the balance of power idea, Britain, France and Russia did a total 180 and supported the revolution for the Greeks. Greek independence pretty much succeeded because of the involvement of these three great powers.

Fallmerayer didnt like this and anti-Greek and later anti-Russian sentiment by men like Fallmerayer led to closer relations between the German states and the Ottomans which lead to economic benefits like the Anatolian railway. Fallmerayer also caused other nations like Bulgaria to advocate for and promote for an ancient connection to Macedon. Greece had basically achieved independence because of the 3 great powers involvement and they helped for 2 reasons one they liked ancient Greece and 2 they wanted to divide the sick man of europe.

Also this historian of Greek history [Vera Sykora] (http://www.uni-leipzig.de/zhsesf/documents/summer_school/Vera_Sykora.pdf) basically states that the whole reason why men like Fallmerayer and William Leake said Greeks have no connection to ancient Greece was because it hurt the western classicist connection to Ancient Greece. Also men like William Leake wanted to take Greek antiquities from Greece and the Greeks wouldnt let them but the Ottomans would.

For a modern genetic take, here is a genetic study of Minoans and their relationship to modern Cretans.

http://www.nature.com/ncomms/journal/v4/n5/full/ncomms2871.html

This chart shows that the genetics of Greeks from the Lasithi plateau are very similar to the genetics of the ancient Minoans buried in the Odigitria Tholos tombs.

http://www.nature.com/ncomms/journal/v4/n5/fig_tab/ncomms2871_F6.html

The PCA analysis also highlights the high affinity of the Minoans to the current inhabitants of the Lassithi plateau as well as Greece. Among the top 10 nearest neighbours to our Minoan population sample, four are Greek populations and two of these from Lassithi prefecture (Fig. 5). The close relationship of the Minoans to modern Cretans is also apparent, when analysis is restricted to populations originating from Greece (Fig. 6b). Particularly in respect to the first PCA (capturing 92% of the variance of this particular subset of the data), the Minoans are extremely close to the modern Lassithi population, the populations from the islands of Chios and Euboea, as well as the populations of Argolis and Lakonia (Southern Greece ) (Fig. 6b). Thus, the modern inhabitants of the Lassithi plateau still carry the maternal genetic signatures of their ancient predecessors of the Minoan population.