You are correct - this issue is only related to the phase detect AF system.
It's normal to get variation in AF. The newest and best lenses have lower variation. Even contrast detect has some variation. The variation is a little larger with phase detect than contrast detect, and on average contrast detect focuses more accurately.
It's also normal for the center sensor to focus more accurately than outer sensors, and the extreme sensors are going to be the least accurate. You fine tune focus with the center sensor - not the extreme sensors.
And with most lenses, the center of the lens is the sharpest area and the edges are softer. That's more the case on FX because DX crops out the outer, softer areas.
Finally, when you zoom on a D800 image, you are looking at nearly double the magnification of D700 and D3 images.