I believe the analogy provided by the evil empire goes as follows:
YWHW prohibited the eating of blood because, symbolically, the blood represents life. Therefore, to sustain one's own life by blood, whether eating it or by a blood transfusion.
This of course is just plain stupid.
You take the life of an animal to eat its flesh. It's dead. So, you sustained your life by taking the life of an animal.
A human donates his blood, but still lives. You take his blood into your veins to sustain your life without taking his. However, that is supposed to be a violation of YHWH's law?
In addition, the analogy is poor because, as I remember, the doctor prohibits his patient from consuming alcohol for health reasons. In other words; if the patient drinks alcohol he dies and if the patient ingests alcohol by IV he still dies. The doctor's orders are not symbolic as YHWH's law is.
In addition, David and his men ate the sacriment bread offered to YHWH at the temple when they were on the lamb from King Saul, which was against YHWH's law. A capital offense. However, David was allowed to eat it as he was starving and needed to sustain his life.