Like Eeveelover said, it definitely doesn't increase the chances/odds/ratio whatever you want to call it. Both pokemon that show up will have a 1/8192 (whatever the number is) chance of being shiny.
I think what auryn is trying to say is that you can effectively trudge through more encounters faster by hunting in double grass. You essentially get 2 encounters for every battle in double grass (assuming the battle was a double battle of course
). So at the end of the day, you will have encountered double the number of pokemon you normally would have for the number of battles that ensued.
Hope this helps