You conclusion is correct. It is mathematically impossible for a non-rational polynomial to have the shape of an exact circle. More generally, any type of ellipse or hyperbola requires a rational polynomial. Parabolic regions can be exactly represented by non-rational quadratics, and hence by non-rational cubics.
So, a standard Catmull Clark subd surface cannot have exact spherical and cylindrical regions. However, typically cubic approximations get pretty close without adding too many control points. If you need exact spherical / cylindrical regions in your model, those regions need to be modeled with Rhino polysurfaces.