Well, I can see some hostility in that post.
Also, I don't see where he implied ownership. After all if someone was talking about Islam and called it "my religion" that would not mean they thought they owned it.
For me, my ancestry is German, Irish, Scottish, English and Cherokee (and whatever else the amateur genealogists in my family have failed to find) and my son is also part Korean. We are all 100% American.
So yes, some of my great-great-great-great-great-etc grandparents were here in what is now the USA.
Not that it matters, really. I mean, what is the time limit on becoming a native? How many generations "allow" you to call a place home? I know that some of my European ancestors have been in this country since at least the early 1800's, and my family first moved to East Texas where I live now during the Civil War.
I am an American. This is my country. I consider myself just as much as an American as anyone from Egypt considers them Egyptian, anyone from China considers themselves Chinese or anyone from Sweden considers themselves Swedish, and I don't know many Americans that feel all that much different than I do about it.