Speed is of no interest for aerodynamics, only dynamic pressure is. This depends on air density (altitude, pressure, temperature) and speed of couse. This means high sped in high altitude might be equal to low speed at low altitude.
What you are probably thinking about is that for most wing sections (airfoils) the pitching moment coefficient is constant over a wide AOA-range. While lifting force coefficient is nearly linearly increasing with AOA in the same range, this still means different center of lift and therefor a total aircraft moment change.
(got it ? The airfoil moment is equal to the moment produced by the distance between center of gravity and center of lift, therefor changing lift means changing this second moment and therefor changing total moment away from the equilibrum)
Therefor any airfoil with a negative moment coeficient is instable althouh the moment coeficient is constant.
So the most interesting parameter for stability is the angle of attack (AOA), you always must have a negative slope of the total aircraft moment versus AOA curve. The AOA change is always depending on a dynamic pressure change for unacelerated flight because lift and weight must be equal. Changing speed alone always results in changing AOA and therefor changing moment. If the plane is instable, this results in a moment changing AOA in the same direction as the speed change did leading to the end of the flight.