Gigabyte support emailed me BIOS F5b for my GA-H67MA-UD2H-B3 and it has fixed this phantom floppy controller issue. After flashing F5b, I went into the Device Manager and the floppy controller was gone. Just to make sure, I did that registry edit that allows you to display devices that were previously connected to the PC, but are no longer connected. The floppy controller showed up in that showing that it was previously connected. I right clicked on it and uninstalled / removed it then rebooted.
After Windows started up again, I went back into the Device Manager and the floppy controller is definitely gone.