We investigate the effects of nonradial line forces on the formation of a "wind-compressed disk" (WCD) around a rapidly rotating B star. Such nonradial forces can arise both from asymmetries in the line resonances in the rotating wind and from rotational distortion of the stellar surface. They characteristically include a latitudinal force component directed away from the equator and an azimuthal force component acting against the sense of rotation. Here we present results from radiation-hydrodynamical simulations showing that these nonradial forces can lead to an effective suppression of the equatorward flow needed to form a WCD as well as a modest (~20%) spin-down of the wind rotation. Furthermore, contrary to previous expectations that the wind mass flux should be enhanced by the reduced effective gravity near the equator, we show here that gravity darkening effects can actually lead to a reduced mass loss, and thus lower density, in the wind from the equatorial region. Overall, the results here thus imply a flow configuration that is markedly different from that derived in previous models of winds from rotating early-type stars. In particular, a major conclusion is that equatorial wind compression effects should be effectively suppressed in any radiatively driven stellar wind for which, as in the usual CAK formalism, the driving includes a significant component from optically thick lines. This presents a serious challenge to the WCD paradigm as an explanation for disk formation around Be and other rapidly rotating hot stars thought to have CAK-type, line-driven winds.