It really boils down to what your eyeballs perceive AZ.
<<I do not have the FULL specification of the specific LED(s) used in my human testing, but they were simply identified by the flashlight distributor who provided them as (as I recall): SST-20 R9080 4000K. They may or may not have the full specification / part number for those devices.>>
One early morning I went to get dressed using a neutral tint (4500k), high cri flashlight and a t-shirt I knew was a gray with a slight hint of green appeared brown. I tried out a cool white 6200k) light and "phew, thank goodness" it appeared normal again.
Now the neutral, high cri light probably got the color a lot closer to correct than one with a lot less accuracy, but the red/yellow bias of the neutral beam persuaded my eyes I was looking at a brown object.
One thing people may not remember about old incan house hold light bulbs was that most of the globes were frosted white in order to present a cooler beam than those with clear globes. Hence the illusion of a cool white beam.