All pedestal sinks have some type of dam designed to prevent water from spilling over the back. Some pedestal sinks, like the one pictured, have a quite substantial backer that obviates the need for a wall backsplash.
So, is this 3" by 6" white subway tile, with border at top, truly a bathroom backsplash? Or is it just a wall? Only you can decide.
From American Olean.
Ice White 3" x 6" tile.