Physical principle of the torque of DC and BLDC motors
To answer exactly half of your question: if the motor had no iron core (i.e., if you made a brushless motor with magnets on the rotor and with only coils on the stator), then the Lorentz force interpretation and the "coil as bar magnet" interpretation would just be two different ways of viewing the same problem.

But as soon as you wind those coils on an armature, my understanding breaks down -- I don't know if all of the motor torque comes from the coils pressing on the armature, or just some (I suspect that it is not none at all).