Gotcha. Thanks for the clarification!
Even with a low CRI, it’s not too hard to make a light that’s indistinguishable, directly, from a blackbody: That is to say, if you shine the light directly into your eye. The catch comes when you see that light reflected directly off of something. In principle, any difference at all between two spectra could make a dramatic difference in the appearance of an object illuminated by those spectra, if you choose the right object. For instance, there are projectors and screens designed such that, when viewed under sunlight, the screen looks black, but when viewed in the light from the projector, the screen looks white (this cuts down on glare and makes the screen easier to view). In practice, the closer the spectra are, the less likely this will be, so folks try to make LEDs with spectra as close to “natural” light sources (i.e., blackbodies, or close approximations to them) as they can.