Was probably buried in accord with regulations for US veterans, which would have included recognition of awards for valor. In this case, the Iron Cross, which was simply depicted with the swastika as it was the way the Germans made the medal in WWII.
I think the Iron Cross motif on head stones was common for German soldiers graves in Germany. Some officials here followed that practice when they buried German POWs in this country. Others did not. At the military cometary in Hampton, VA. the head stones of 55 German and Italian POWs buried there are identical to the ones used for American service personnel buried there. The only difference is the word “German” or “Italian” carved into the head stone.