Increasing lift with airspeed, for a given alt, moves COP back.
80kts at 4000 ft is the same lift as 100 kts at 4000 ft. AOA of 80kts is higher, lift is the same, COP more forward. Did a forward COP create more lift in this scenario? Nope. Lift = Weight in both cases.
So the conditions of flight seem relevent when you consider a broad brush statement such as this.