If the autofocus system of the D4, D800, D800E, or D600 is activated by pressing the shutter release button down halfway, which is the default configuration of these cameras, the focus priority works as expected, because if [Focus] is selected at either Custom Setting a1 [AF-C priority selection], or Custom Setting a2 [AF-S priority selection] the shutter is disabled until the camera has acquired focus, in other words it is not possible to take a photograph unless something in the area of the viewfinder frame covered by the AF points is in focus.
Many Nikon photographers, especially sports, action and wildlife shooters prefer to use the AF-ON button, or one of the configurable buttons of their camera to perform the AF-ON function, to activate the autofocus system, so it is decoupled from the shutter release button; however, Nikon has altered the protocol in respect of focus priority when autofocus system of the D4, D800, or D800E is activated by the AF-ON button, or in the case of the D600 when the Function, Preview, or AE-L/AF-L button, is assigned the AF-ON function, via Custom Settings f2, f3, or f4 respectively.
This is a significant, yet undocumented modification by Nikon from all their previous DSLR cameras, which has not only caught out many photographers, but also led some to believe their camera(s) had a fault.
On the D4, D800, D800E, or D600, if the AF-ON button, or a button assigned the AF-ON function is used to activate the autofocus system, the camera disregards the selection of [Focus] at Custom Setting a1 and a2, and the shutter will operate regardless of whether the camera has acquired focus, or not. Consequently, it is possible to take a picture that is out-of-focus in either the AF-C, or AF-S focus mode, when the selected AF priority is [Focus].
It appears that Nikon has decided to assume that if a photographer uses the AF-ON function in preference to the shutter release button to activate autofocus, then they know what they are doing, and will control the AF system of their camera accordingly. You have been warned!