Blood flow, normally laminar, can exhibit high frequency fluctuations suggesting turbulence, which has important implications for the pathophysiology of vascular diseases and the design of blood-bearing devices. According to the classical model of turbulence in a homogeneous fluid, these fluctuations can be attributed to the cascade of eddies down to the Kolmogorov length scale, which, for apparent turbulence in blood, is reported to be on the order of tens of microns. On the other hand, blood is a suspension of mostly red blood cells (RBC), the size and concentration of which would seem to preclude the formation of eddies down to these scales. Assuming dissipation occurs instead via cell-cell interactions mediated by the plasma, here we show how turbulent velocity fluctuations, normally ascribed to turbulent (Reynolds) stresses, could give rise to viscous shear stresses. This may help to resolve fundamental inconsistencies in the understanding of mechanical hemolysis, and it provides a physical basis for the forces actually experienced by formed elements in the blood under nominally turbulent flow. In summary, RBC must be acknowledged as equal players if a satisfactory definition of turbulence in blood is to be achieved.