This is a bit astonishing.
Re-reading this thread that I started, only now do I realise that Mode-C sends back flight levels that are then converted into altitudes
by the radar software - and that my instructor did not have a clue about this fact!
When I was advised not to use Mode-C under a CTA, I was a student; the transponder was a steam-gauge one and the reason given that it was not accurate made some sense to me, at the time.
After getting my license, I got checked out on another aircraft, with a Garmin digital transponder that shows you the offset between actual and pressure altitude, and the advice became "Don't use Mode-C as it's set on 1013 mb and cannot be changed, which gives wrong altitudes most of the time", leaving me with the unanswered question as to why they would build Mode-C transponders that are useless most of the time...
The advice "Ask your instructor, instead of relying on an internet forum" doesn't always apply...