What they are talking about is the pitching moment about the aerodynamic centre of the aerofoil. By definition the aerodynamic centre is the point on the chord line about which the pitching moment does not vary with changes in angle of attack.
But this constant pitching moment is true only when measured about the aerodynamic centre. If you make a small model of a cambered wing (or even a flat one - a small sheet of card or balsa wood does nicely) ) you will find the when released at a slight nose down pitch attitude it (usually) tumbles in a nose up direction. This indicates a nose up pitching moment about its C of G. But when attached to an aircraft with a forward C of G the moment about the C of G of the aircraft will be nose down.
To visualise what is happening to the C of P you need to look at those diagrams that illustrate the pressure envelopes above and below the aerofoil at various angles of attack. As angle of attack increases the C of P of the upper surface envelope moves forward, while that of the lower surface moves aft. Until you get very close to the stall both the uper and lower envelopes are decreased pressure (we might call it suction). So the
movements of the upper and lower C of Ps causes an increasing nose up pitch.