Same with me...upgraded from 8 to 8.1 but when I did so, lost the ability to refresh my PC because I didn't have the 8.1 install media. MS really stepped on their genitals with this.
But in the article, you first download 8 and enter the product key for 8. As soon as they verify the PK and the download begins, cancel it. Go back to the update page and select download 8.1; this will get you the 8.1 OS. Once you have this, you'll be able
to make 8.1 install media for refresh operations AND you can install directly to 8.1 without needing 8 first. When it asks for the PK, use your Win8 PK.
I've read reports that people are having issues with the upgrade and certain apps and that a direct 8.1 install seems to be the key. Still, I think MS is really going off the deep end because 8.1 is NOT a new OS vs. Win8, but more along the lines of them
fixing Win8 (as in, this is a SP). For MS to act like this is a new OS is truly cringe-worthy.