Recent comparisons between experiments and computational fluid dynamics (CFD) simulations of flow in the Food and Drug Administration (FDA) standardized nozzle geometry have highlighted the potential sensitivity of axisymmetric CFD models to small perturbations induced by mesh and inlet velocity, particularly for Reynolds numbers (Re) in the transitional regime. This evokes the classic experiment of Reynolds on transition to turbulence in a straight pipe, which can be delayed, apparently indefinitely, if special care is taken to control for external influences. Such idealized experiments are, however, extremely difficult to perform and, in the context of cardiovascular modeling, belie the "noise" inherent in typical experimental and physiological systems. Previous high-fidelity CFD of a canonical eccentric (i.e., non-axisymmetric) stenosis model showed transition occurring for steady flow at Re ~ 700-800, with modest delay caused by the introduction of shear-thinning rheology. On the other hand, recent experimental measurements of steady flowing blood and blood-mimicking fluids in this same stenosis model report transition for Re ~ 400-500. Taking a cue from the FDA nozzle controversy, the present study demonstrates that the addition of small-magnitude random noise at the inlet brings the eccentric-stenosis CFD results more in-line with experiments, and reveals a more gradual transition towards turbulence. This highlights that, even in non-axisymmetric idealized geometries, unnaturally "clean" high-fidelity CFD may impede not only good agreement with experiments, but also understanding of the onset and character of blood flow instabilities as they may exist, naturally, in the vasculature.