The ancient Greeks themselves considered the Trojans (of the Trojan War era) to be Greeks. Dionysius of Halicarnassus even stated that Troy was ‘as Greek as any true Greek city’ (something like that; I don’t remember the precise wording). This belief is displayed in the Iliad too, where the Trojans are presented as having the same language, culture, and religion as the Greeks.

Obviously this doesn’t fit the reality of the Mycenaean era, since the Greeks only settled Troy from c. 900 BCE. But then, plenty of chronological information about the Trojan War actually places it post-900 BCE (like the evidence from Ctesias).