Okay, that has solved the problem, though I have been using my method for years, and do not recall having this problem before (the fences did not "unhide" when I double clicked on an icon in a hidden fence).
It does bother me, that when my fences are unhidden, I don't get a clean lined up grouping of icons inside and outside of the fences. Outlook 2016 is not in line with OneNote 2016 (in the Fence). Not vertically for the top of the screen, not horizontally anywhere. "No, I don't have OCD, I prefer CDO because it is just better in alphabetical order."
Also, sometimes when the computer restarts or "wakes up" , some of the icons have moved to the empty space on right side or above the fences, even though the Fences have not moved.
Last night I did not turn off my computer, so it went into hybernate. When I "woke it up" this morning, this is what I saw. I had left the Desktop in the state of the first picture. The MicroSoft Apps Fence is in the same location, but there is apparently no longer any room for the Outlook icon to the right of the fence (visible or invisible) Same with the fence below it (Graphics, Video & Audi) which has "crowded" Magix Photo & Graphic... icon to a previously non existent empty space above the fence. You can imagin what this looks like when I hide the Fences. I have to manually fix this everey time I restart or "wake up", which is way more work, than just double clicking to get rid of the initial unwanted "Unhide fences" snafu.
I realized something else today as I was restoring my intended layout of Icons and Fences. When the Fences are in an "unhidden state" (so visible), and I double-click on an icon in a Fence, this is not seen as a double-click to hide the fences. However, when I double click on an icon that is excepted from being hidden IN a Fence, that IS seen as a double click to unhide the fences. See, the logic escapes me, plus it seems like the effect of a double-click on an icon IN a Fence can be recognized and ignored, but the programmer just forgot to apply that condition to this set of circumstances. Once again, I don't remember ever having this problem before I installed Fences on my new computer two months ago. Also (again): I don't know if it did occur, and I just didn't notice it. However, it seems like something that should be included in the next update, because the method of placing excepted icons outside of Fences just creates a mess. I will be undoing this in a few days.