For the last several Olympics at least, typically the closer you get to lighting the flame, the more prominent the torch-bearers become.
In the 1996 Atlanta Olympics, for example, Al Oerter (underdog winner of four gold medals in four consecutive Olympic games) carried the torch into the stadium.
From there, he handed off to Evander Holyfield, who runs around the stadium with a cute *Greek girl (whose name I do no recall).
They then handed it off to four-time gold medalist swimmer Janet Evans.
She then runs the final leg of the relay, handing it off to Muhammad Ali.
In the 2002 Olympics, the torch was lighted by the 1980 Olympic hocky team. Eric Heiden had won five gold medals in those games.
Was he invited to participate, and just turned it down?