Costs of having a US-based PhD supervisor doing a PhD in Germany? A little background first, as this is maybe not familiar to people outside Germany: In Germany there are universities that can not award PhDs. So called "Hochschulen/Fachhochschulen". This means they have to cooperate with a university that can award PhDs at which the student is then enrolled as PhD student and also has an official PhD supervisor. But the work (and in practice most of the supervision) is done at the "Hochschule". Also notice that in Germany getting a PhD is normally "thesis only", so no course work. Also in this setting the student already has a Masters, which is a requirement in Germany for starting a PhD.

If someone wants to partner with universities in the US to get a PhD, will the student have to pay regular fees / tuition even if it is "thesis only"?

Or do you even need to be officially enrolled at the US university if you have a professor there who agrees the supervise you?
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.