What looks strange to me about all this is you can restore an System Image (Windows 8 using Windows 8 recovery media) without any keys and it is already activated and ready to go, assuming you made the image after you activated.
That image can be put on a clean hard drive, so some of the problems that seem to have been encountered in this thread do not make sense. It may not want to re-image a Windows 8 image to a hard drive with 8.1 already on it.