I am either misunderstanding you (I did ask a few questions, so I am not sure which you are answering) or we are just in complete disagreement on semantics and reading capabilities.
"'At common law, with the nomenclature of which the framers of the constitution were familiar, it was never doubted that all children born in a country, of parents [plural] who were its citizens [plural], became themselves, upon their birth, citizens also. These were natives or natural-born citizens, as distinguished from aliens or foreigners. ..."
There is the declarative statement of the paragraph. That specifically defines what constitutes the parameters that make a "natural-born" citizen. It is followed by a statement that recognizes that "others" have held forth an expanded view of what constitutes a "citizen."
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.
He makes his point, which goes directly to the issue, in the part I bolded. His aim is to underscore his first point so that the second issue (what "others" have said about citizenship in general) is not confused as having anything to do with the main issue.
"For the purposes of this case, it is not necessary to solve these doubts. It is sufficient, for everything we have now to consider, that all children, born of citizen parents within the jurisdiction, are themselves citizens."
The third statement in the paragraph sews up his argument about the status of the subject before the court. That there is no doubt about his citizenship. He isn't trying to establish that he is "natural-born" just his citizenship in general. It only happens, by virtue of the facts he presents, that the criterion of "natural-born" status was described in the first statement.
When he says "there have been doubts" he is not stating a precedent in law he is stating that "some" have held different views regarding "children born within the jurisdiction, without reference to the citizenship of their parents." That is a true statement. There were different views about that.