Point well noted Cobalt. The wording of the text (in the English translation at least) is crystal clear, so it surprises me when authorities such as the Irish and UK CAA still publish misleading summaries.
Yes, definition of "operator" may cause some difficulties, but only for owner pilots of small aircraft. In the case of larger types the operator of the aircraft is required to hold "operating approvals" in order to operate, for example, in RVSM, MNPS airspace etc.
The holder of any such "operating approval" would have little difficulty, IMHO, proving that he/she/it is the operator of the aircraft, and where he/she/it resides.