Rubio was not born of American citizen parents. So he most definitely would NOT have been considered a citizen of this country, much less a natural born citizen of this country, by Mr. Bingham.
Mr. Bingham says “of parents owing allegiance to no other sovereignty”. He didn’t say they had to be citizens. It is pretty clear from their actions at the time that they had no allegiance to Cuba, and they confirmed that by becoming naturalized citizens.