I posted this before, in this thread, which has some example images.
Ed Giorgianni once told me that, in the film days, a wedding photographer sent him a picture of the husband-to-be, the best man, and all the ushers. The image had been made on color negative film. All were wearing black tuxedos. None of the tuxedos was black in the picture. None of the tuxedos was the same color as any one of the other tuxedos. Ed said that the black aniline dyes used to dye clothing are strongly reflective in the infrared, and that the three layers of the film had some sensitivity there. The result was a disaster for the photographer.
The solution to IR problems is the same in digital capture as in the film days: UV- or IR-cut filters over the lens or the chip, or both. The IR-cut filters that come on most cameras are inadequate for some combinations of subject matter and illumination.
The IR case can be thought of as an example of the larger problem.
The more variables you setup to build your anecdote the less it provides consistently predictable, accurate and usable data to mitigate against when creating better looking pictures. Film does not come very close to reacting/recording to light as a digital sensor. Editing 3000 Raws vs about 100 scanned negatives told me that.
One of the major variables not mentioned here and in Andrew's linked Doug Kerr pdf (which offered plastic vs paint illuminant reflectance variances in kitchen devices as his anecdote) is the fact that sensors only record/measure voltage charges in grayscale that get redefined by software as color on an RGB display after those grayscale measurements go through the A/D converter. The display's RGB filtering of those grayscale pixels would have to be known and compared against the sensor's RGB spectral transmission filtering to know exactly where the errors occur.
All in all we're no where close to mitigating this issue and just resort to selective color editing as we've always done. Out of the 3000 Raws I've shot under lights of extremely varying spectra, I really never seen this as a big problem to overcome in the post processing stage. The blue/purple flower example Jim Kasson linked to doesn't really prove or point to the source of the causality with any consistency because I've shot similar flowers and sometimes they're purple and sometimes they're blue shot under the same light.
I do notice this blue/purple issue with flowers whenever I've been out too long on a hot day and my batteries are going low which points to a heat issue but still no proof or consistency in coming up with attempts to avoid or correct except in post processing.
I just think there are WAY too many variables that haven't been considered to know for sure this illuminant metamerism is the cause to consistently mitigate against.