Looking into this, it appears that it's most likely a Microsoft glitch. According to their official documentation here:
https://docs.microsoft.com/en-us/dotnet/framework/migration-guide/how-to-determine-which-versions-are-installed
The proper way to check for the framework is to check the version number from the registry, and check to make sure it's at least 460798, which I've confirmed is what we're doing. I'll do some further testing on Windows 7 to confirm that it's not broken in general, but I'm afraid MS might have just screwed the pooch on that system and somehow something got corrupted.
@rexryan If you're okay with diving into the Windows registry, you can go to Computer\HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\NET Framework Setup\NDP\v4\Full\1033 and check the value of the Release node to see what the version number is. I'm guessing it's somehow incorrect. You might try uninstalling and re-installing the latest framework to see if that fixes the issue.
My apologies for the trouble @rexryan.