Recalling a video I have seen (forgot the source), the actual damage wouldn't occur upon hypoxia, but upon re-oxygenation. Lack of oxygen at the cellular level does start a fatal chemical reaction, but the structure of the cells are largely preserved. But when you put oxygen back, everything blows up (or swells up, actually).

Harry may very well have killed Hermione with his oxygen shot. If he froze her before then, it might have worked, but after that… her information might be lost.

One obvious objection: Hermione was still concious enough to say some last words, ruling out advanced brain de-oxygenation. That could be only for the drama, but still.

One obvious consequence: that magic feeling upon death might be linked to plain muggle information-theoretic death somehow. But then, we have horcrucxes and Avada Kedavra… I'm quite confused by HPMOR's "laws of physics".