Hi
So you have a receiver connected to an ESC which then drives the motor (brushed or brushless?)? I'd be surprised if the ESC presents that much of a load to the receiver, to cause the output voltage to drop like that, though I admit I haven't looked at it. But how are you measuring? The output of each channel of a receiver is not a straight DC voltage - it's a variable width pulse. The pulse width varies according to the intended servo position (or ESC output, in this case). I can't remember the precise details, but it's in the order of 20ms. You'd have to be looking at a scope to see the pulse amplitude.
Similarly, the ESC is PWM'ing the power to the motor varying between pulses too short to actually overcome the inertia of the rotor, which just makes the motor 'sing' at the PWM frequency, to 100% duty cycle. The MOSFETs are fully on or fully off. Then the actual current drawn depends on the load on the motor - high angle of attack 3d stuff draws welding current. You couldn't measure that meaningfully with a multimeter.
I have an Eagle Tree data logger which records info over the course of a flight, and can tell you volts/amps/watts with time and average over the flight. Very useful for checking when things are going wrong, and for finding efficient pitch/throttle curves.
Sorry if this is all obvious.
John