Costs of having a US-based PhD supervisor doing a PhD in Germany?
Even when cooperating with a German university, the candidate will be subject to any terms or requirements given by the "Promotionsordnung" of the university. (It is true that many of those do not require any additional coursework, but there are formal criteria to meet nonetheless).

Therefore I assume that, also in your envisioned scenario, the student would have to meet any formal requirements that the US university usually imposes on their PhD candidates. This may include not only paying for, but actually taking the coursework for example. The fact that the German "Hochschule" may be satisfied with "thesis only" work will not be relevant then if the US university is the one awarding their degree.