Not sure but I wonder if it is just that the III has the processing power to handle the update and the II didn't. Regardless, when I was researching the III I saw a bunch of post update reviews and...

If your renting an A7r, try to rent one of their GM lenses. I've got the 24-70 GM and love it. If you end up liking the A7R and buy used go with the III as there was a firmware upgrade back in...