On December 29th, Nikon acknowledged the problem and stated they were working on it. This morning Nikon announced that starting at the end of the month, they will inspect and service at no cost D750's light-shielding components and adjust the AF sensor position. (See story update below.)
“To users of the Nikon D750 digital SLR camera
Answer ID 19336|Published 12/24/2014 11:36 AM|Updated 01/09/2015 01:02 AM
To users of the Nikon D750 digital SLR camera
Thank you for choosing Nikon for your photographic needs.The issue can be generally be eliminated with the use of a lens hood, but on those occasions when a photographer wants to use lens flares artistically, such as in contre-jour photography, it can't be controlled. Moreover, when using wide angle lenses with short, squat hoods, the flaring shows up despite the lens hood.
On December 29, 2014, we announced that we were looking into measures to address the issue reported by some users, namely that when photographing scenes in which an extremely bright light source, such as the sun or high-intensity lighting, is positioned near the top edge of the frame, flare with an unnatural shape sometimes occurs in images captured with the D750 digital SLR camera.
To correct this issue, Nikon will inspect and service at no cost the camera’s light-shielding components and adjust the AF sensor position. We plan to initiate this service at the end of January and will announce further details, including instructions for requesting servicing, shortly.
Please direct inquiries regarding this matter to Nikon Customer Relations by phone at 1-800-Nikon US (1-800-645-6687), 9AM–8PM EST, Monday to Friday (closed certain holidays) or online here.
We sincerely apologize for any inconvenience this issue may have caused, and ask for your continued patience and understanding.
Once again, thank you for choosing Nikon for your photographic needs.”
The problem's apparently caused by the camera's autofocus sensor module at the bottom of the mirror box. On D750's in which the flaring and dark band occurs, the sensor unit protrudes from the bottom more than it does on cameras that are fine. It appears the protruding sensor affects how the light reaches the sensor.
For more details take a look at the PentaPixel article “Nikon D750 Owners Reporting a Dark Band Problem That Causes Ugly Lens Flares.” Nikon Rumors has a report on this problem too.
It seem pretty clear that Nikon has learned from their D600 debacle, when they took far too long to acknowledge the problem, and offer a free solution for it. Nikon got on top of the D750 problem within about a week after the report of the problem and the reason behind it became well known, and now has offered a solution less than a month since the first reports became public.
Update: After consulting with several stores we now know that Nikon has recalled the stock of the D750 remaining in their authorized dealers' stores. Amazon no longer lists the camera on their website, suddenly Adorama has the D750 listed listed as “out of stock” and B & H Foto & Electronics Corp lists the D750 as “backordered.”
(Image of the Nikon D750 courtesy of Nikon Inc.)