So I thought about it some more, and I realized I explained it pretty badly. Ohm's law is relevant, but only as modulated by the controller. At low speeds (not limited by current saturation of the inductive windings) and at full throttle, all those smart electronics in the motor driver impress a full-voltage (though probably current-limited) sine wave across the motor coils, at the proper frequency and phasing for the motor's rpm and instantaneous angle. Under those circumstances, yes, V = I * R, and the higher your battery voltage or the lower your motor's winding resistance, the more current the motor will draw and the more torque and power it will put out (until the driver current-limits you).
Anything other than full throttle, the motor controller is delivering a lower-amplitude voltage waveform to the motor winding, still pretty much beautiful sine waves (that's the point of all that smart elx), but lower in amplitude, so V = I * R still applies, but the applied voltage is less than the battery's maximum. That's what the controller does. It produces a drive voltage proportional to throttle opening.
But always, the phasing and frequency of the output sine waves (which are generated by very fast digital switching waveforms to the drive IGBTs or MOSFETs) have to be precise to achieve high efficiency. That's what this "motor commissioning" business is all about -- achieving that precision so the motor can be as efficient as possible.