It wasn't necessarily inadequate as much as it was inconstant. There was a dip due to the lung damage, but then there was reperfusion afterward as a result of medical treatment.

Sometimes, when tissues are deprived of oxygen, they undergo apoptosis when the oxygen is restored, not when they are deprived. This is why people who undergo heart attacks are sometimes rapidly chilled to core hypothermia. The cold discourages their tissues from committing suicide when their power comes back on.

Her extremities might have been saved by putting them in ice baths, but it is very unlikely her physicians would have been aware of the potential problem and quick enough to respond appropriately. Their primary concern was likely maintaining sufficient oxygen to her brain and vital organs.