I WOULD
!
I too have heard of (but not witnessed) a passenger ride in a Racing Caterham with no second seat or belts present - on a well known British circuit with a race driver and..
I too have also never witnessed any form of scrutineers inspection on testing days, on any circuit up and down the country even while I was helping a manufacturer - I'm sure they are only present for competition excluding maybe DB check?
That said if I was to give tuition I would want to make sure the seats and harness were safe.
ALSO as pointed out on a testing day ie: Novice cross - I would be concerned as a driver, if it does go pair shaped, "even on a testing day" all of sudden the same MSA / FIA rules used by scrutineers for racing may suddenly apply under investigation?
Still clocking up posts to get that avatar.. LOL