I just found out that my new shiny cheap lab PSU is 5% to 10% off !
It has a nice resolution but the readings in both V and A don't match my measurements with an external multimeter...
The model AX6002P from Axiomet is similar to the better known Velleman or KORAD KA6002P so it might be a known issue....
My "golden tester"'s battery is a bit low (8.5V) so I changed with a fresh one (curious since I changed it less than a year ago).
I tested the measurements against other multimeters, checked the power supplies and ... all values are coherent within the respective accuracies.
Bad battery. Case closed. Sorry for the alarm. But the question is still good and it would be cool to be able to calibrate the device "if something happened" :-)