So it seems to be a translation issue indeed.
In the German translation of the regulation, the term "Entgelt" is used, which, in German legal jargon, includes any form of payment or "consideration", even towards the cost.
Re the different countries involved, just trying to clarify that for my own case: If I fly a German (D)-registered plane in Germany, does it matter that I'm a UK-license holder? Would I, for example, be limited by the "pro rata" cost sharing requirement (which doesn't exist in German air law)?
Regards