Not sure who he said (not watching) but Robert E. Lee owned it. Lee’s wife was Mary Custis, who inherited it when her father, George Washington Parke Custis, died. Custis was grandson of Martha and was adopted by Washington after his father died.
So Washington had a round about connection to it, but don’t think it was ever owned by Washington, but with the huge land tracts in those days, who knows. http://www.smithsonianmag.com/history/how-arlington-national-cemetery-came-to-be-145147007/
Arlington was seized by the Union from Lee during the Civil War. It was returned to him afterwards but he sold it back to become Arlington National Cemetery.