Driving in a curve (make it infinite if you will: a circular track) your tyres will try to hold you glued to the road, and the centrifugal force ("doesn't actually exist", yadda yadda -- but it works for the purposes of this discussion) will try to push you outwards.
The tyres exert their force at road level, the centrifugal force at the height of the CoM. The CoM usually being above road level, the centrifugal force will tend to tilt the car outwards.
Lower the CoM to exactly road level and there is zero tilting moment; your car might slide outwards if it loses grip, but it will remain upright with no tilt, because the centrifugal force has no vertical leverage relative to the opposing gripping-force of the tyres -- they're opposing each other in the same horizontal plane.
Lower the CoM below the road (magically travelling through the soil without interacting with it), and there is again leverage, only this time with the centrifugal force pushing outwards below where the car is trying to stay attached to your desired trajectory and thus tilting the top of the car inwards, towards the inside of the curve or the center of the track.
:: Moving the CoM down has a stabilizing effect down to road level, but if you go lower than that it starts destabilizing again, only applying its rolling force in the opposite direction.