Cell salvage macines are usually used in surgery, so it wouldn't be strange if the staff on the delivery floor did not know how to operate one. When the jws talk about all these 'alternatives" to blood transfusions, they forget to let you know that there is no guarantee that they will be available at any hospital.
The poor woman died because she refused what could have saved her, the transfusion of packed red blood cells. They were available and I am sure the staff knew how to administer them.
They want to blame someone. After all, their god did not save her and the family is left with the blame. Sad.