[TigersEye]

"Some authorities go further, and include as citizens children born within the jurisdiction, without reference to the citizenship of their parents. As to this class there have been doubts, but never as to the first.

It is only speaking of doubts about citizenship. It is saying nothing at all about considering them natural-born.

[Rutabega]

How on earth do you read that this means they might not even be citizens? It means that they might not be natural born citizens, but they might be. Show me anyone who says a child born on US soil to parents who are not either in the army of another country, or its diplomatic corps aren’t citizens.