I did a little digging and, it appears that Mitsubishi and CoeLux have partnered on these artificial skylights and, although the CRI isn't listed, the CoeLux site says this:
"CoeLux systems combine LED lighting that reproduces sunlight spectrum, direction and brightness with optical systems and nano-structured materials that reproduce the endless distance of the sky and sun."
If it actually does reproduce the sunlight spectrum it'd have to have a very high CRI, no? Toshiba has their TRI-R LEDs claimed to be capable of 95% of the sunlight spectrum and they are rated at a CRI of Ra97. Yuji has LEDs with claimed CRI of 98, so it seems within the realm of possibility that these fake windows are very convincing.