As this is a new PC build (only 10 days old), no it has never worked.
Interesting thing though, if my desktop resolution is set to 1024x768 @ 88hz, then when I launch a game at 800x600, it runs at 60hz. If my desktop resolution is set to 1024x768 @ 85hz, then when I launch the same 800x600 game, it runs at 85hz... (and not, it's not a quirk with that specific game)
EDIT: After doing that testing, any game in fullscreen at 800x600 now wants to run at 60hz instead of 75hz...
EDIT 2: I was able to get 800x600 running at 75hz again by deleting my 800x600 @ 112hz custom resolution, rebooting, adding a custom resolution of 800x600 @ 85hz, and then finally rebooting again. Once 800x600 @ 75hz was working again, I was able to delete my custom 800x600 @ 85hz without consiquence and was even able to add my original 800x600 @ 112hz back in.
EDIT 3: I re-created the 60hz issue and tried the steps in my "EDIT 2" to see how repeatable it is, but it didn't work this time...now I'm stuck with 60hz for 800x600. It may have been because I tried a custom resolution of 800x600 @ 75hz instead of 85hz to see if that would also work (it did not). Now I do know that if I re-install the graphics drivers, things will go back to defaulting to 75hz rather than 60hz.
EDIT 4: Here's something interesting, those 800x600 fullscreen games of mine will always run at 60/75hz unless my desktop resolution (if not set to 800x600) has a refresh rate of 70hz, 72hz, 75hz, or 85hz. If I use any of those as my desktop refresh rate, then regardless of the resolution of my desktop, any 800x600 fullscreen games will run at that same refresh rate.
EDIT 5: I think I've figured out why a custom resolution and refresh rate of 640x480 @ 120hz works - it would seem that, 60hz, 70hz, 72hz, 75hz, 85hz, and 120hz are all refresh rates that the Intel graphics drivers deem "acceptable" for use. I say this because if I change the refresh rate for my 640x480 custom resolution from 120hz to 144hz, then any 640x480 fullscreen games will instead run at 75hz, just like what was happening with the 800x600 fullscreen games. Note that I also tested 90hz, 96hz, and 100hz, but none of those were considered "acceptable" because 640x480 fullscreen games were still running at 75hz.