Thats tricky. I know the heat exchange components are called radiators but most of the heat they give off is by convection not radiation. (At least here on the ground.) I heard 80%-20% rule of thumb.
But you are right in the broad strokes. Cooling is not easier in space. Mostly because you have no convective heat transfer.
I can help explain why. On earth, we are surrounded by stuff. Radiative cooling relies on thermal radiation leaving an object. Crucially, it also requires the object to absorb less thermal radiation than it emits. On earth we are surrounded by stuff, including air, that emits thermal radiation. There is a window of wavelengths, called the atmospheric window[0], that will allow parts of the thermal radiation out into space, rather than returned back. Imagine shining a flashlight on tinted glass, the light will get through depending on the color. If the light gets through, it has escaped. If not, the light is returned and heats up your surroundings again.
Also on earth the other methods (conduction, convection, and phase changes) are more effective. The earth can be used as a very big heat sink. On a spaceship or satellite, you don't have the extra mass to store the energy, so radiative is the only option.