Correct. Location does not matter.
If geography was a factor then theoretically the King of England could become President if he were born in a US hospital or any other American site. That is a ludicrous notion but it would be consistent with the argument that being born on our soil is all that matters.
Sir Winston's mother was American. Too bad he never ran for President. He'd have made a far better one than the Doofus on the Dime, not to mention the incumbent.