Why are German Hospitals interested in international patients?

The point is, that German government has been trying to cut the annual budgets which hospitals get for the treatment of social security patients (90% of total hospital patients) over the past ten years. Essentially, the budgets were frozen, regardless of the annual rise in expenditure due to pay increaes etc.
One of the very few ways for German hospitals to make a little extra income besides the government-regulated budget is the treatment of non-social security, independently paying patients from abroad. Some hospitals have put a great effort into trying to increase this venue of revenue, like forming little "private clinic" within the big hospital structure. They have built special luxury facilities with additional standards. Treatment in these private clinics is of course rather costly - but the luxurious standard makes it worthwhile for anyone who can afford it. Other hospitals offer the same medical standard, but only the normal accomodation standard (which is usually two patients per room, single rooms are available for a moderate surcharge). This is the choice for patients who are interested primarily in the medical expertise of the physicians who are going to treat them.
In addition, the treatment of international patients is also a source of additional revenue to the physicians themselves. At least in most cases they have contracts that allow them the treatment of "private patiente" as private practicioners.