I actually have this issue with a 50" plasma I use at times. The screen could only do 59Hz not 60.
Let me start from the beginning on your questions.
The idea behind pulling the vsync setting out of the game and into the control panel was to isolate if there was a bug in the game software that it just was not getting the setting to the driver (not the case per your testing)
The idea behind changing the vsync cap to something other than 60 hz was to see if you had a change (you did). This isolates 2 things. If it was a change to fixed then the problem was that the hardware could not draw at 60 hz (believe it or not some screens use one 60hz driver on different quadrants and only do 15 or 30 fps....). If the change resulted in some other change to output that made it worse then it could be a frequency misalignment.
A frequency misalignment can be for several reasons but think of it this way. The TV is trying to draw at specific pulses once per frame by taking the data in the tv memory and displaying it all at once. Screens no longer draw one pixel then the next then the next the way they did with CRTs and 1 electron gun hitting each pixel. Whatever is in the memory will be displayed to the screen. Now think that the card is trying to draw at 90fps and the screen is drawing at 60 frames per second. if you think of the screens coming from the video card as 1, 2, 3, 4, 5 etc then at the first impulse for the screen (@ 60Hz) the card has drawn 1.5 frames. So the first half of the memory has the second screen and the second half still has the first screen (tearing). this exact 1.5 difference will result in tearing at the midplane of the display.
Now the same thing can happen on a smaller scale. Imagine the TV says it is displaying at 60fps but it can only do 59fps. This can be because of a hardware difference in the oscillators (the clock) and can be temperature dependent. Then you will tear at a different point every draw. Or if you can only draw 59.9fps then you will tear sometimes and sometimes you won't...
There is a lot of hardware and software designed to prevent the clocks from getting misaligned, but it still happens. If it didn't then we would never need things like vsync etc. Sometimes the difference is odd and even the software and hardware attempting to vsync can't accomplish the task... That is why when it really comes down to it they let you slow down the refresh rate.
You may need to just try different rates that work for you....
BTW beware the cheap 4k displays (TVs). they are 1080p drivers hooked to multiple pieces of the display and can not run at 60 fps for the whole screen in 4k mode....
Hope that helps explain all your questions.
