Stone of all types are used as backsplash, so in this case the naysayers are wrong. There is nothing wrong with using granite for both the counter and the backsplash, it's done all the time and it looks fine. The one thing I will add to this is that the area can look a little "monolithic" with all that stone. To add interest and design, you could tile the backsplash with a complimentary colored tile and incorporate trim tiles and/or specimen tiles for something a bit different.
You should be able to find all sorts of examples on-line of both granite BS and tiled BS. Look through a few and see what strikes your fancy. Oh, and when asked if you want the full splash to continue behind the stove/cooktop, YES! Absolutely, YES, you want this!
I suffer from CDO ... Its like OCD, but in alphabetical order, LIKE IT SHOULD BE!!!