.. y'know I've had this problem too.. I never figured out why but since I was not planning on rendering the wrap deformer object itself.. I left it alone. In my case the wrap deformer was a poly mesh.
I imagine wraps are most often used as 'free-form' lattices, and so they flip the Primary Visibility flag off for you on that assumption ...but why they leave you with a viewport solid i dont know (i usually kill shading) ...guess its if your animating low-res character wraps, or if your using wrap deform objects as lumps of influence points rather than as point tweaking lattices.