Player models work differently than other models in q3/trem. In order to facilitate an easy method of switching around textures on player models, a *.skin file is used which describes what textures are applied and where for each different skin. All other models used have the paths to the textures hard coded into the *.md3 file.
So, in order to use any player model stuff in your map, you need to re-import the *.md3, and recompile it with a specified path to the texture you want it to use.