“So is every naturalized citizen every much a citizen as a natural born citizen”
Clearly, no. Naturalized citizens cannot be president.
But they can come and go from the country. IOW, if the goalpost is "citizen," amenable to entry to his country, then naturalized citizens are every much a citizen as a natural born citizen. Immigration makes no distinction between them. For purposes of the case in hand, all who bear the title "citizen" are equal; regardless of how they came to that title.