'High speed' is matter of perspective. In general, particles in all phases are capable of moving very fast, but speed can also be thought of in terms of net movement. Also, given enough energy, all particles are capable of moving fast.
In simplest terms, liquid particles are incapable of moving fast, if we are thinking in terms of the net movement of liquid. In a liquid phase, particles are bound to each other, not as tightly as in case of solids, but not as weakly as in case of gases. In general, the liquid particles slide past each other, thereby giving liquids the ability to take the same shape as the container they are in. The particles in gas phase are capable of moving at fast speeds and achieving actual net movement. Thus, the given statement is false.
Hope this helps.