Following are the reasons why it is more likely to work pulling a radio stream via MC than pushing it from MC...
It looks like the renderer is actually pulling a playlist from MC (rather than a track), and that playlist itself contains one of more URLs of remote radio stream(s). So the renderer is probably dereferencing the playlist and pulling the internal radio stream direct from the remote server URL. (You might even be able to turn off MC at this point and the radio stream might even continue to play). It would depend very much on the individual renderer whether it has the capability to dereference playlists. (My DMRA tool would probably be able to tell you more about what your particular renderer can do...)
On the other hand, MC is not able to push playlists. It tries instead to dereference the playlist itself and push each track directly. And since it has no way of proxying the radio stream track, nor of handing off directly to the remote server, then it cannot push a remote URL from itself. (It would be a neat feature to consider adding though...)