"Hagel, to my knowledge never tossed his medals over the White House fence as Kerry infamously did. "
Actually, Kerry kept his medals and, as far as I know, still has them. What he threw over the wall was a ribbon rack. A medal is attached to a ribbon, but also comes with a ribbon section (same color scheme as the one on the medal itself) that is usually work on all working dress uniforms in lieu of the medal itself. Ceremonial dress uniforms are the ones actual medals are worn on. (In the Marines and Army, these are dress blues, and in the Navy officer ranks, would be choker whites. ) Medals worn around the neck (like the Medal of Honor) can be exceptions to this rule.