How to choose the right potentiometer for dimming a LED
Furthermore I remember that current vs light given by a LED is heavily
  non-linear. That means that if I manage to cut the current in half the
  light will not be half but probably 1/4 or even 1/5. If I'm not wrong
  again.


It is actually directly linear to the current (once you factor heat variation), but what is not linear is the eye response to light intensity.

The driver might not drive the LED in DC mode but perhaps in PWM mode. PWM mode allows to increase the power output of the LED, as it is flashing faster than the eye response, if you have a duty cycle of 20%, you can power the LED at 5 times higher for the same "load" (with abstraction to losses) and the eye will perceive a much brighter light as it only sees the "on" state.

If you want to DIM the IKEA LED, you need first to understand the driver schematics.

Adding a potentiometer before the driver won't work.
Putting a  potentiometer within the LED strip it will probably overheat as potentiometer are not designed to dissipate power. Also the driver will regulate the current, so increasing the impedance probably won't work.