Brushless DC Outrunner Motor Control
First, as somebody else pointed out, ESC stands for Electronic Speed Control, not Engine Speed Control.  And BLDC motors do not experience any slip.  They are synchronous motors. 

Second, the quote you gave is confused.  BLDC motors don't have a "DC" rotor.  They have a permanent magnet rotor.  "DC rotor" would only make sense if the rotor were wound.  The quote isn't wrong that the higher the stator frequency, the higher the speed.  But it is misleading because speed isn't controlled by frequency.  

BLDC motors are identical to brushed permanent magnet DC motors in how they are controlled.  Increase the voltage, increase the speed.  Increase the current, increase the torque.  The difference comes in how they switch the current in the coils as the rotor rotates.  The act of switching current from one coil to another in a motor is called "commutation."  In a PMDC motor, the switching is done mechanically with a commutator and brushes.  As the rotor turns, the brushes come in contact with different bars on the commutator and that causes the current to switch coils.  Note that the faster the rotor turns, the faster the current switches from one coil to the next.  

BLDC motors do the same thing but instead of mechanical commutation, they use electronic commutation.  The commutation brought into the control so that transistors do the current switching instead of the commutator and brushes.  With a PMDC, the timing of the switching was mechanically determined by the width of the brushes and the shape and number of bars on the commutator.  With a BLDC, the timing has to be determined by the control.  This is done by determining the angular position of the rotor with either an encoder, Hall effect devices or some other means (ESC's are often "sensorless" and estimate the rotor position based on voltage or current waveforms).  Note that just like in PMDC motors, the faster the rotor turns, the faster the current switches from one coil to the next.

I hope you see that the frequency is a result of the speed, not determined by it.  The switching of the current from one coil to the next occurs when the control "sees" that the rotor has changed angular position.  So, yes, the frequency of switching does change as speed changes, but the frequency does not control the speed.  

Third, you are right that there are many different forms on control for BLDC motors.  The control method I describe above is often called a "six-step) or "trapezoidal" control.  But you could have sinusoidal or field-oriented control (FOC) as well.  Most hobby grade RC brushless ESC's are six-step controls.