I don’t think that is the issue. Roosevelt’s point is that Jackson had dual English American citizenship.
While we generally accept that Jackson was born a long the South Carolina/North Carolina border back in 1859 there were questions of whether he was actually born at sea.
Jackson was born in 1767 somewhere in the Carolinas. His parents emigrated from Ireland in 1765.
I'm not sure if the South Carolina constitution had citizenship requirements or not, so I'm assuming that Jackson and his parents were considered citizens of the United States in 1789.
-PJ