the circuit is driving the inductor at the resonance point of the circuit, with the duty cycle adjusted for critical damping of the waveform (one overshoot, one slight undershoot, then nulls out). The 12V is HIGHLY regulated and isolated so there are no negative currents. I wish I could share more of the circuit with you, but this was a very special project, and not even my 80W minuature radar replacement switchers I did for the FAA took this much work or design effort. Leave it to say that under certain conditions, inductors do crazy things. Tesla knew this, very well. You don't always need a secondary winding to get a large voltage jump. For instance, the reason you need the snubber in the first place...
It is just as meaningless to blindly pick a snubber at 2x without knowing what frequency, inductance, etc of the circuit being driven, but it's done every day by 'rule of thumb'.