Neither a Natural born subject nor a naturalized subject could ever grow up to be KING. This is why Black's is not comparable. Everyone born in England was a subject to the King. What did he care, it was only more people to collect taxes and fight in his wars.
Our founding fathers were worried about infiltration and especially British subjects wheedling their way into power and then undermining everything they fought for in the Revolutionary War. They most clearly were concerned with people having been born with dual loyalties getting into the presidency and then taking us to war or using America with other countries interest in mind. And at worst they were worried about sabotage.
It's pretty simple. With England they didn't worry who they labeled a "natural born subject" because that person would never be in position to ever do any real harm.