I wholeheartedly disagree.
I don’t think the Founders would have added the clause “or a Citizen of the United States, at the time of the Adoption of this Constitution” That clause grandfathered in those who were not born in the Colonies. The Founders were clear regarding subject to the jurisdiction thereof.
They didn’t say subject to British, Kenyan, French jurisdiction - ie to be inclusive. They were clearly being exclusive of other foreign jurisdictions.