Revolve Cut Doesn't work?

From what I understood, revolve cut would revolve a profile about a straight line only. This would mean that if I were to revolve-cut a rectangle out of another rectangle, the cut edge would be straight and perpendicular to the line revolved about. Apparently this is not the case; at least not for circular shapes. I'm modeling a sphere that is built out of individual pieces. To model the pieces, i start with the sphere and revolve-cut one axis, then the second axis (as seen in the model attached). I thought that the second revolve cut would give me a revolved cut about the line I chose, but unfortunately I'm getting a parabolic shape instead of a straight line. This suggests it's not really rotating about the line I chose. Any information that could shed some light on this subject would be greatly appreciated.