Are you sure? If z is distributed over the surface of the sphere there is far less surface at the extremums -1 and 1. Doesn't z being uniform in the range (-1,1) lead to points being actually more densly concentrated near the poles? Or did I misunderstand what you meant?
Near the poles the surface becomes very flat and therefore there is as much surface area in a slice of constant height than anywhere else. Archimedes was a clever fella :-)
