Is the new governor of RBI not an Indian?

Govt names US citizen Rajan RBI Governor

In an IMF speech delivered as a Pravasi Indian, he says

"The highest elected office of the country is open to anyone who consciously opts for Indian citizenship, not just to those who are unthinkingly born into it. All this reflects a willingness to assimilate, and work with, that which is foreign in the broadest sense of the term."