For a positive cambered airfoil, the moment is negative and results in a counter-clockwise rotation of the airfoil. With camber, an angle of attack can be determined for which the airfoil produces no lift, but the moment is still present! So for airplanes with regular wings the tail has to press down because wings will try to rotate counter-clockwise and CG is aft of AC and opposes rotation.
The Moment coeficient however is constant over AoA, or therefore constant over Cl. So only at low Cl (low AoA, high speed) the moment is dominating requiring a negative stabilizer lift. At high Cl (high AoA, low speed) the lift of the wing dominates over the moment, so although the airfoil is positively cambered, lift might be produced at the stabilizer in this condition if the AC is ahead of the CG.
And by the way, being constant the pitching moment does only affect pitch equilibrum, but not pitch stability.