While doing some manual AFMA testing on my 5D3 (firmware v1.1.3), I noticed a peculiarity about focusing in LiveView - the camera ignores the AFMA setting, and will even not report any AFMA value in the EXIF data! My old 50D always used the AFMA data.
After looking into this a bit more and thinking it through, the observed behaviour seems correct and to be expected. When the camera is in LiveView, the image sensor is used to directly observe the focusing where the focusing is needed and therefore you don't need to adjust for any tolerances between the lens/AF sensor complex vs the image sensor. Thus, you always get the optimum focusing
The downside is of course that focusing in LiveView is much slower than when using the normal AF sensor.
This the 5D3 and 1Dx share so much on the AF side, I assume that this applies to the 1Dx as well. Confirmations of this observation on both 5D3 and 1Dx is appreciated.