Hmm. Actually, I'm not sure why German students would want to study medicine in the US... I've never actually seen a European med student studying in America. I suppose they may want to do it if they choose to live here, but I've never seen that, either.
In terms of treatment, the glorification of the US system is a bit overblown. The Europeans certainly have cutting edge technology and excellent medical care which is equivalent and can exceed US treatment. In fact, in the area I work in, cardiology, Europeans are often more innovative, being the system that employed drug eluting stents, radial approach to cardiac interventional procedures, and transcatheter aortic valve replacement, just to name a couple things.
Given the fact that the US gets care that is at least as good in terms of quantity, yet doesnt cover their population completely (even post-ACA), and it does this at a cost of about 50% more to double that of the cost of European nations. That, my friend, is what is called 'inefficiency'.