Not sure about that one, but he did, I believe, drive Lee Harvey Oswald’s mother to the police station that infamous day in Dallas...(please, someone correct me if that’s wrong.)
“The Star-Telegram newsroom was virtually deserted that morning as all working reporters had raced to Dallas to cover the tragic story. Still, recalls Schieffer, the phones were ringing off the hook. One call he took he will never forget. It was Lee Harvey Oswald’s mother and she needed a ride to Dallas. Schieffer and the paper’s automotive reporter borrowed a test car and drove her. To this day, he doesn’t know why she called the paper. Perhaps it was because she had once worked as a governess in the home of Star-Telegram founder Amon Carter’s son. Schieffer still recalls that the distraught Mrs. Oswald seemed oddly more concerned with herself than with either her son’s plight or the death of the president of the United States.”
I believe you are right. I've heard Schieffer telling that story on a couple of occasions, and I think that's what he said.