Blood transfusions are given for patients whose hemoglobin or hematocrit level fall below established guidelines. A hematocrit below 30 is where things get worrisome. Without adequate red blood cell levels, oxygen can't get to tissues and tissue hypoxia sets in.
People can walk around with hematocrits lower than 30 but they will feel like crap. Part of my job as a laboratory manager was to perform blood draws on patients. Once when I took a tube of blood for a red cell count from an old man, I could see from the tube that he was very anemic, so I took an extra tube for blood bank testing and ran his blood count right away, even though the doctor had only asked for one-day turnaround. The doctor ended up ordering 2 units of packed cells that day. Whole blood is usually only given in cases of bleed-out through trauma or injury where volume and not just red cells have been lost.
I learned from having worked at a hospital with a very aged population what "thin" blood looks like as it is coming into the tube. I was encouraged by other lab employees to take an extra vial of blood while the needle was in, for blood bank testing if the need should arise for a transfusion that day. It saved us a trip and another poke.
Transfusions do carry risks, as not all viruses can be caught. The blood is tested, but if there is one virus particle in the bag, there is no assurance it will make it into the small drop that is tested. The risks to the patient if they don't have the transfusion are probably uppermost in her doctor's mind.