[The_Reader_David]

No, the fact that another country’s laws regard a person as having given up U.S. citizenship has no weight whatsoever under U.S. law.

As a reductio ad absurdum of position that it does, imagine that a revolutionary government took over a country and decreed that all persons inside the country when the new government was instituted were citizens, and that it did not recognize dual citizenship. That action would not strip U.S. citizens of their U.S. citizenship under U.S. law. U.S. citizens escaping back to the U.S. would not need to be naturalized.

[aruanan]

No, the fact that another country’s laws regard a person as having given up U.S. citizenship has no weight whatsoever under U.S. law.

The example you used is not quite reductio ad absurdum because it is not an extension to the nth degree of a particular situation but the creation of an entirely new one, the only similarities being governments and declarations of citizenships.

Besides, you're ignoring the other part: A minor child's citizenship follows that of the custodial parent, at least for the period of time in question.