Once the Auto-focus Mode and Auto Focus Area Mode settings are dialed in, they don't change until you go in and change one or the other; switching between Exposure Modes (P, S, A, M and Auto) does not alter the auto-focus settings in any way.
This is interesting, as her camera did not do this. She shot for two days in Auto mode with AF set to Auto-AF and Auto point select. No focus issues, just the depth of field we started with.
After observing the really high shutter speed with middling f-stop, for the next day I had her change to Shutter priority of 1/250 (enough to freeze motion and eliminate movement on our boat and/or hand shake) which would force (on bright days) a better f-stop. We did not change anything in the AF system. The next day, almost all (but NOT all) her shots were out of focus and she complained that the "focus boxes" seen the day before were no longer visible in the viewfinder. I was in hot water, so she changed back to Auto mode and focus was as before. This leads me to question either your statement or the performance of our D7000. The manual seems to agree with your statement as does other stuff I have read. Comment? Has anyone verified that it works that way?
PS - As part of this quest, I updated her camera to the latest firmware version (A-1.03 & B-1.04). No mention of focus in them but just better to be up-to-date.
Another aside - I do not usually shoot in Auto mode with my D800E, and have had focus problems (why I previously read the Mansurov article). So I wonder if this goes across different cameras? Maybe it is in the settings?
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New information: I found a reference which introduced the "AF Custom Settings" choices. It is in the "Custom Settings Menu" (pencil icon). There were a couple of settings which contributed to our confusion.
Setting a1 which is AF-C priority was set to "Shutter" meaning it would take a photo upon shutter release whether it was in focus or not. Changed the setting to "Focus" meaning the photo would not be taken until focus was achieved.
Setting a4 which is "AF point illumination" was set to "Off" meaning the camera would NOT illuminate the focal point in the viewfinder (one of our specific problems). Set it to "On" so we will know the focal point.
All the other settings seemed okay to me. We ignored this part of the manual because we didn't think we needed to make "custom" settings. Wrong! We will see how this works in further tests. Fingers crossed.