And in addition, and TFA alludes to this, each time a person receives a transfusion there is a chance that their immune system will generate antibodies to it. That might not impact the transfusion at the time, but can make the recipient much harder to match for in the future.
My partner has had severe anemia, and because of a prior transfusion went from being an easy match (A+) to a being a 1 in a thousand match. The last time she needed blood it took 12 hours to locate and transport suitable blood.
If you read the literature on survival rates for people with very low hemoglobin level, it's all based on post operative recovery (or otherwise) of Jehovah Witnesses
The blood rejection is reaction between blood plasma (with cells produced by your immune system) and red blood cells.