Fibrin is a protein formed from fibrinogen in the blood, strands of which glue platelets together to create a blood clot. Fibrin is therefore essential to stopping bleeding (haemostasis), but it can also cause unwanted clots inside blood vessels (thrombosis) and will cause blood taken for transfusion to coagulate unless steps are taken to prevent it. One such step is defibrination.
The first human-to-human blood transfusion was performed by James Blundell in 1818. He found that blood could be transfused successfully, even via a syringe, if the operation was concluded swiftly. Any delay risked coagulation. Various devices were invented to address the problem, including J.H. Aveling's direct transfusion apparatus (1872), but the use of defibrinated blood became the favoured solution. Typically, blood was defibrinated by constant agitation in a container full of glass beads.
The idea of "blood so pure that we need not defibrinate it" appears to be medical nonsense.