It is true that red blood cells, when mature, are anucleate, or without nuclei, meaning they have no DNA to replicate.  When they are newly produced, from the bone marrow, however, they do possess nuclei, so perhaps it is the younger cells that are used in DNA fingerprinting.  It should also be noted that blood samples are not the only body fluids used in DNA fingerprinting, among others, saliva, urine, and semen are valued highly in terms of compiling DNA fingerprints.  So that would be my best answer, the use of "new" RBC's, which do possess nuclei, and therfore possess DNA.