Strange Denti, must be a German thing...
PIC is the one who is the highest authority onboard, and the representative of the company and State of Registration. That is ICAO and Common sense.
There can be more than one Captain onboard, but only 1 Commander PIC.
Actually very simple.
Linechecks are checks to see the proficiency of the crew, ultimate responsibility lies with that crew unless the checker officially takes command in case of an absolute