This is standard nationalist rhetoric--the nation is eternal and never dies, it just lays dormant under oppressive occupation. Arab nationalist rhetoric often says the same thing about Ottoman "occupation". You might see Ukrainians saying the same thing about Russian-Soviet "occupation". If places like Scotland or Catalonia or the Basquelands or even Cornwall break away, they will all argue that their nation has a unique, proud, and continuous history.

This presumes that we should live in a world of nation-states, and ignores the fact that these are quite new--arguably Spain, England/the UK, the Netherlands, and France start behaving like nation states in the early modern period [see Phil Gorski, Anthony Marx, and Liah Greenfeld's work], but the conventional turning point is France after the French Revolution. There was no Greek government in exile. There was no remnant of the Byzantine Empire (which, let's remember, was Greek-speaking Empire which claimed to be the successor state of the classical Roman Empire; not a Greek nation-state) that remained. The Greek elite, especially in the old Byzantine capital of Constantinople/Istanbul (which was the center of Greek-speaking culture, not the backwater of Athens), were very involved with running of the Ottoman Empire.

If that presumption is true, then did cities like Istanbul/Constaninople and Smyrna/Izmir and Trebizond/Trabzon, all of which entered the Ottoman Empire with Greek majorities and left (as part of the modern Republic of Turkey) with Muslim/Turkish majority cease being "occupied" Greek cities and start being a real part of the Ottoman Empire or the Republic of Turkey? To a historian, that idea is a rather absurd claim that relies heavily on nationalist assumptions.