Color temperature and CRI are unrelated, from my understanding.
You can have a warm 3500 LED or a Cool 5000 LED (probably closer to sunlight at noon) but both can have poor CRI scores.
The color temperature stuff is still being studied. There are definite negative repercussion to blue lighting at night. That is why we see a trend towards Red and Amber LEDs for camp setups. LEDs are all on the higher color spectrum and are then covered with filters to warm them up a bit. Halogen naturally preserve your night vision better than any LED or HID. There is another side to night illumination that is being overlooked because of new/hot/trendy/profitable tech that uses less power.
This picture sums up how CRI works pretty well.
View attachment 3131492