Nikon USA has issued an update to its communication around issues with flare in some D750 camera bodies. Following a statement in late December that the company was 'looking into' the matter, Nikon has announced that it will inspect and if necessary service affected cameras at no cost. Reading between the lines, Nikon's statement appears to support the hypothesis that in those cameras which have been affected by flare, it is caused by the position of their AF sensors. 

The service will be initiated at the end of January and further details are contained in Nikon's statement (below). 

Nikon statement:

Thank you for choosing Nikon for your photographic needs.

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 or online here (global support information can be found 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.