But I don't say I'm Scottish-American. I say I'm American because I live in the United States.
Your way is to say Greek-American because you thrive on the attention of being Greek, if you aren't "trolling" us again.
Actually this is part of why I see America as deeply racist. The term African-American is used to the point black Africans sometimes get called African-American. Sure black Americans can be proud of their heritage but they are just American. It's this racially dividing term that is unnecessary, as you pointed out Irish-Americans never refer to themselves as Irish-American, just American with Irish ancestry, and there is a lot of Irish Americans.
Similarly it is fairly popular here in Australia to call people who act actors, some avoid using the term actress since it is pointless and sexist. Actor means "someone who acts", not "a man who acts".
Oh yeah on topic- I am from Earth. Residing in Australia.