First, I want to say that long ago I shot a D2h, circa 2004. That camera has what I euphemistically call "most distant subject priority focus mode". The camera only has 11 AF sensors and they are very large, extending well beyond the focus reticle marks.
I determined, with careful tests, that given a choice of two subjects, one more distant than the other, the selected sensor would focus on the distant subject even if only a tiny part of the actual AF sensor was off the close subject.
When I upgraded to the D300 and added a D700 that problem went away. I have shot 200,000 images with those cameras and never suspected that there was any tendency to choose distant subjects. I believe this is an old problem Nikon long ago fixed.
I don't have your camera but I would be surprised if Nikon reverted to their old, poor logic. And that is supported by the fact that I don't see other complaints of this nature.
Carl Sagan is famous for suggesting that "Extraordinary Claims Require Extraordinary Evidence" or something to that effect. As I recall, it was in reference to UFO's but my experience is that it well applies to AF issues .
That is a joke of course. I know AF issues can be very troublesome and frustrating but they are very hard to pin down, and, more importantly, it is even more frustrating and difficult to convince others in the case where you think your camera behaves uniquely.
With that in mind...
I downloaded 6 of your NEF files from your FTP folder- 701_0404/405/517/1009, and 710_0929/0930.
I viewed each in ViewNX, displaying the active focus point. None of the 6 indicate a focus point. This, I think, is critical to your problem and your examples.
There are a number of reasons why the focus point is not indicated, and it varies somewhat from model to model. I just re-studied this issue and found variances in how my D300 and D700 deal with this. I don't know the "rules" for your camera.
However, in general, when using AF-C Release Priority Mode as I believe you did, and AF-On, the AF points should always be indicated if a) the camera believes the subject was in focus and b) you are actively focusing.
Actively focusing means that in the case of using AF-On only (shutter button does not focus), the Af-On button was pressed at the instant the image was captured.
If the AF-On button was not pressed when the shutter fired then some models will indicate an AF point if the active sensor saw a focused target, but others will not. Neither of my cameras will indicate the active focus sensor info if focus is locked, for example, with a programmed focus lock button. You would have to test your own model to get to the bottom of that.
You said that you are not using a tripod. If you tripped the shutter without pressing AF-On, you may have recomposed by accident. You may have something in your shooting style that is confusing the issue. Remember what I said about extraordinary claims .
I am not suggesting you did or didn't shoot these correctly. I am, though, suggesting that you need to at least reproduce the problem with sample images that have an active AF sensor indicated in the EXIF. Otherwise you could not convince me, and likely no one else, without doing that.
I would not accept images without that EXIF confirmation even if I shot them. So don't take that personally. From long experience, I never question images that do not have that EXIF indication. I know in that case I likely did something "wrong", in some sense.
Access to ViewNX may be problematic for you, but I think you need to work something out in order to solve this problem. You need that feedback.
Afterthought: even if you can not get ViewNX working, your camera should have an LCD playback option to display the active and used sensor (if it indicates anything). That is just as useful as ViewNX except you are looking at a tiny 3" image instead of something easier to drill down into on a large screen. Check your camera menus; it may not be turned on by default.
For the sake of process of elimination, one possibility, in principle, is that your actual AF sensors are out of line with your viewfinder reticle indicators. A test is fairly simple:
1. Set your camera on a tripod. You MUST use a decent tripod for this test. You need to eliminate any possibility of accidental focus/recompose.
2. Find a target, something like a stop sign, with simple geometry, and with a fairly distant background such that focus is absolutely unambiguous. I think I used a tree trunk for my initial D2h tests but followed up with better targets to confirm my theories on that camera.
3. Now take different shots, some squarely on the target, and some bordering the target. You may not even need to take shots, except as extraordinary proof to convince others. What you see in the viewfinder should tell you all you need to know.
You will also learn the extents of the actual focus sensors verses the viewfinder reticle indicators. I find very little overflow on my D300 and D700 but others seem to think there is more than I do.