but I don't understand how the the inductor (which would have very low DC resistance?) would stop the capacitor from drawing the initial large current from the DC-DC converter? What am I missing?
You are missing the fact that the effect of an inductor is to slow down rapid changes. So when the current rapidly rises the effective resistance ( inductive reactance ) is high but when it slows down to DC it is low ( just the resistance of the windings ) which is exactly what you want.