I think of level designer basically the same as I do an interior designer. The best interior designers often make their own furniture or art pieces when they have to, to fulfill a particular vision for a space, but they don’t have to, most of what they need to do their job is “off the shelf” or they might work with a craftsman who augments them.
So I don’t think a level designer needs to be a artist/modeler as well to be successful, but I certainly think knowing both aspects gives you the potential to be a better designer.