I have a D600 (and D800) and I don't see any green shift. There is a slight difference in the LCD image - but it does not appear green to me.
The comments from Larry and others are accurate - you would not use the LCD for critical color, it can be adjusted, the image may not reflect the LCD, and adjusting the image color to fix your LCD to personal taste is heading down a really wrong path.
Color from the D600 is better than earlier cameras. The new generation of cameras and processors seems to get more out of the image sensor - not just low light performance but better dynamic range and color at low ISO levels. DxOMark is the bet source of sensor information I've seen. They don't get into anything about the LCD display since it is not relevant to the final image.