pilotwolf, your posting ist absolute correct but not fully complete. There are many exceptions.
The 3 german language countrys, Switzerland, Germany and Austria have a „Memorandum of Understanding“. This contract contains simple Licence Regulations.
Example:
A Swiss with a permanent Residence in Switzerland can flight a German Helo in Austria.
Only if a Swiss has a permanently Residence in Germany, then he must convert his Swiss-Licence to an German Licence.
And all other combinations, of course.