If I saw an ethnically Chinese or African person who said they were Greek, I would ask, "where do your ancestors originally come from?" because it's clear that they weren't plying the Aegean in the days of Homer, running amphorae of olive oil from Samos to Corinth. Ethnicity and nationality are two distinct categories that in the modern world are frequently confused or conflated. Someone can become a Greek national but not a Greek. This was the point of the article in The Economist.

In Russia, for example, where ethnicity is a required line in a person's passport, the term российский (rossiyskiy) is used to denote Russian nationality, and русский (russkiy) to determine ethnicity. Thus, a Chechen in the Russian Federation can be considered as гражданин Российской Федерации (grazhdanin Rossiyskoy Federatsii, a citizen of the Russian Federation) but never, no matter what he does, will he ever be listed as русский in his passport because that is an ethnic classification. The same thing holds true in Kazakhstan, where one can be a Kazakhstani citizen but not a Kazakh (unless one has been so since birth by accident of ethnicity).

Not only that, but other than some extreme exceptions, I doubt that most of the recent immigrants to Greece are Orthodox Christians, or drink ouzo, or can dance the sirtaki, or know how to cook traditional Greek dishes, or could cite lines from classical Greek literature or the Byzantine period, or understand most of the cultural mosaic that Greek culture has passed on from generation to generation. It is entirely possible that their children might become more Greek, and that their grandchildren will be totally assimilated, but it is not a necessary conclusion.

Holding a passport without any connection to the culture and people of a nation creates a valid basis to question the propriety of allowing such an individual into a nation in the first place. While not all immigrants fall into this category, I suspect there are enough economic immigrants in Europe generally to help create animosity, particularly if the failure to assimilate is plain to see and brazen.