It depends on how closely scribed your counter is. Backsplashes are usually there to hide and cover the gap between the counter and the wall. If you can minimize the width of that gap and then caulk it completely, you don't need a back splash.

If you look at the photo closely, you can just barely see a horizontal line about 24" off the countertop. With the slight green tint below, I'd guess they used a sheet of glass as a backsplash, which is fairly common when one doesn't want 'busy' tile in a clean lines kitchen.