Dmitry, Pete, I've checked the issues addressed by the updates to the D4 firmware and found the update A/B 1.02 addresses the following issue:
"Gamut for Adobe RGB images displayed in the camera's monitor has been changed. This enables more vivid display of images."
Of course, in Nikon's own inimitable style, Nikon has said the D4 LCD displays are more accurate and set to have a better color reproduction than previous DSLR models. They also said that the display color temperatures in the older D3s/D700 models were slightly higher which made the images to appear somewhat bluish. In other words, Nikon is claiming the green tint problem for the monitor isn't and wasn't there. And of course, they still may have addressed it in the update.
I've never noticed the problem, but then I normally don't really look at the color rendering of images in the monitor as an accurate depiction of reality. I look for it to be off in a gross way which would indicate my white balance is off. I'm shooting in RAW, and I therefore address the color rendering in the photo in post processing anyway.
For the purposes of this thread, (I have A/B 1.02 installed) I looked critically at the monitor and I personally see no green tint problem in my monitor (or my photos for that matter).