I think it's just a learner's mistake, but quite easy to understand their real intention which PROBABLY is to get in touch with an English native speaker.

I'm Canadian which, I suppose makes me an American of sorts. Still, I would never call myself that. To me, an American, is a person who lives in the political entity called the United States of America. I would not suggest you call a North American native (meaning indigenous) person an aborigine. You might get a punch in the nose! In Canada, we often politely call them "First Nations" people. This may be  because we don't know the name of the tribe they are part of (or can't pronounce it).  Many of them call themselves Indians, by the way, which is a problem because there are a lot of people from India around. Recently an indigenous friend of mine called himself a native American although he is Canadian, like it or not.  By default, people from India are often called Hindus even though some of them are Sikh or some other religion. Oh dear. 

Recently, I asked a couple of people with strong accents, "Where are you from?" only to have them say, "Vancouver". Of course, I am asking about their country of origin. Apparently this has recently become an insulting question. Oh dear, again.

People usually say native speaker. But as for native American, any person born in the territory of the Americas after the establishment of the americas is a Native American. Because most of the people being described as Native Americans did not live in a place called America, they are not Native Americans but natives to that area. But this is like most modern politically correct uses of words and terms that rarely take into account proper title. I guess nobody cares. Native Japanese sounds normal to a modern Japanese person, but like most countries in the world there were people living there before, that are not related to the current inhabitants. I doubt a Native Rhodesian would want to be called a native Zimbabwean.

Good thinking Emma! I agree with you...