Well I've had 3 D800s and they all had this issue. The first two I sent back to the dealer but the 3rd I sent to Nikon UK with pretty much the same results as the OP. Nikon UK don't make you pay for postage, but given their abysmal customer service, I suspect this might be to do with UK law. I find it hard to believe it has anything to do with Nikon's goodwill ( of which I have yet to see any evidence ).
Anyway, it came back worse than ever. The left AF point was all right but all the others were off by varying degrees. The centre point was absolutely awful!
I phoned Nikon who gave me some waffle about high resolution being responsible. They took it back again and it came back no better. I had bought it from Amazon who warranty their electrical good for a year and so I returned it. I was extremely disappointed with Nikon's service and attitude. I don't think I've ever had such a poor experience from a major company.
I haven't tried another D800 since. I might next year to see how well I do in the Nikon lottery but I'll make sure that I buy it from Amazon again. At least you can trust them to serve their customers which is sadly not the case with Nikon.
TBH I feel a bit of a chump for switching from Canon to this dreadful company.