I agree that the law makers cannot write the law any other way than to make the pilot responsible for a wrong flight ID. But that doesn't absolve the examiner from his duty to leave the plane just as he/she found it.
Because let's be honest, most private pilots will hardly have a clue what a mode-S transponder really is, compared to a mode-C transponder. They look and feel exactly the same and the only real difference, at a first glance, is the price tag.
The fact that mode-S emits a flight ID, that this flight ID is normally your callsign but that, under some very specific circumstances, it could be something else, is something most will not know.
Yes, you can argue that a pilot should know how to operate all equipment in the aircraft, but a 20-hours/year pilot who rents aircraft as and when required, realistically will not know how to check and set a flight ID. Particularly since the flight ID is normally not shown on the display.