Interesting.

If the measure is on the battery side, the current is DC amps and is not an average value. ESC converts the DC to AC to drive the motor, and hence the timing or frequency of the AC comes into play.

Edit. Just checked the manual for CC Phoenix HV series of ESC. There is a current-limiting feature. The default setting (normal) will allow moderate over-current condition and enters the shut-down mode after a slight-delay.