Of course, that's to be expected. But, we have to ask a brave question? Why does it matter? Genes (DNA) don't carry cultural and historical memories. Your genetic ancestors' greatness (we never talk about their negatives) isn't passed as memories through DNA. It's the ideas, the civilization that you may feel proud of, but then all this is available to anyone. I don't have to be English to appreciate British literature, philosophy and science. Same with the Hellenic civilization's goodies.
You, anyone can feel Hellene, or modern Greek, or love Greece, etc. Several ethnic groups rose against Ottoman rule. Many didn't speak (nor understood) Greek. I doubt that all knew about the Hellenic past. But, circumstances and geography made a nation out of these diverse people in the 19th and 20th centuries.