And you would be wrong. Read it again and pay closer attention to that little clause beginning with "that may".
"And the children of citizens of the United States that may be born beyond sea, or out of the limits of the United States, shall be considered as natural born citizens: Provided, That the right of citizenship shall not descend to persons whose fathers have never been resident in the United States:"
It says clearly that "children of citizens of the United States ... shall be considered natural born citizens" --- even though they may be born overseas.
Thus "jus sanguinis", birth to American parents [plural] was the determining factor of natural born citizenship to them.
Come on, do you seriously think “that may be born beyond sea, or out of the limits of the United States” means that provision also applies to children born inside the United States? Is that really how you read statutes, or just the ones where you’re trying to read it to say what you want it to say?
It certainly does extend jus sanguinis citizenship to children born outside the United States. Now where does it deny jus soli citizenship to children born inside the United States?