For what it's worth, I had this issue and did a little bit of digging into it. In my scenario, I had a previous install of Minecraft, but recently had the hard drive it was installed on die, and had to reinstall it on a different hard drive. After receiving this error when both trying to uninstall the nonexistent old version and when trying to install a new version, I opened regedit and proceed to use the "Find" tool to delete any reference of "Minecraft or Mojang." I'm sure there's a more precise way of doing this, but brute forcing it this way seemed to work after a restart, and I was able to install as normal.
Incarnate
For what it's worth, I had this issue and did a little bit of digging into it. In my scenario, I had a previous install of Minecraft, but recently had the hard drive it was installed on die, and had to reinstall it on a different hard drive. After receiving this error when both trying to uninstall the nonexistent old version and when trying to install a new version, I opened regedit and proceed to use the "Find" tool to delete any reference of "Minecraft or Mojang." I'm sure there's a more precise way of doing this, but brute forcing it this way seemed to work after a restart, and I was able to install as normal.