The motors do see that voltage, but not constantly. The current to the motors is constantly switched on and off at a frequency up to 20 khz(pwmulse width modulation).
Because the coil of a stepper motor reacts slow on current changes, the average curent will be the motor rated current. The high voltage is needed for good performance at higher speeds.
When you are running at high stepfrequencies with a low voltage the current in the coil of the stepper wont have the chance to reach its nominal value before the current is switched off to energize the next coil (high step freq.).
To get a full understanding of this I sugest that you have a look at the following text: