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.

In the situation you describe, you're not really having an external supervisor. You're a PhD candidate in a university and your research happens to be conducted in a Fachhochschule. The central issue as you said is that the Fachhochschule isn't accredited to deliver doctoral degrees.

So what you are asking is: can I join a graduate program in a US university and conduct research in a German Fachhochschule. I'm not saying it's impossible, but it's seems like a very long shot.

• First you will need to be accepted in a graduate program with (presumably) a Bachelor from a Fachhochschule. I think just that is going to be a major obstacle, especially if you're aiming at a prestigious institution (see: Is it realistic to apply to a Master at MIT, Harvard, Yale, Berkeley, Stanford with a Bachelor of a German Fachhochschule?)
• Then IF that works out the Fachhochschule’s requirements will be irrelevant. You will in many cases have courses requirements, have to pass quals exams, and all other requirements from the US graduate program. Hardly compatible with you living on another continent.
• The research typically conducted in Fachhoschulen can be very different (typically more applied or translational) than what is done in universities. It might be hard to meet the university's standards for a PhD thesis.

Specifically to your question "will the student have to pay regular fees / tuition even if it is "thesis only"?" the answer is quite probably yes. Usually graduate students and their supervisors seek funding to cover all costs including tuition and stipend.

Maybe you should re-think your strategy and possible try to do a Masters in a German University first. Then applying to a US graduate program might be more plausible. Alternatively you could look at having co-supervision with a professor in a local university.