That's a puzzle to me as well. Always thought the hotter the temp, the higher the number. 6500 or around there is supposed to be sunlight, I thought. Perhaps it's a difference between the color temperature of something as opposed to the temp of the light bouncing from something. Though now that I wrote that, isn't that the same thing?
It's almost confusing as colors of light and colors of paint, if you mix all primary colors of light, you get white and if you mix all primary colors of paint, you get black.