Not quite. If I recall correctly the tail will move about 1/2 degree per second. Hardly the speed of light. The elevators are hydraulically operated and can go much faster, but hydraulics don't move at the speed of light, either. The 3000 psi refers to the hydraulic pressure in the system, which has kinda nothing to do with how fast things move. Boeing considered going to a higher pressure to save weight, but rejected the idea because a pinhole leak at such pressures would act like a knife on human skin.
Source: I worked on the horizontal tail design of the 757.