It's true in a literal sense. Former New York University running back Ed Smith struck the famous pose for trophy sculptor and childhood friend Frank Eliscu in 1935.
It's also true in a historical sense. The award was mostly given to running backs during its first half-century. From 1973 to 1983, only running backs received the trophy.
But the Heisman's status as mainly a running back trophy started to fade, and then the 21st century completely wiped out that notion.
Since Ron Dayne won the award in 1999, only one running back has won the Heisman Trophy—Mark Ingram, the offensive star of Alabama's 2009 national championship season.