That was an interesting show, and a lot of good arguments against that tired old piece of apologetics... but I was aiming at a different point.
All these points - pro and contra "dying willingly for a lie" - only take into account the victim, never the killer. Why do people assume that these were all the nice rational people who would have gone "Oh, so you deny Jesus now. Fine, scuttle off! Sorry to have bothered you!"?
From the Christian side it is understandable: if you believe that martyrs only and exclusively were killed for "preaching the truth", there would be no reason not to let backsliders go off.
But if there were - and there were! - other reasons: political, economical, social - for persecuting groups... it is very likely that just denying your faith would not left you off the hook.
The pious martyr just makes a better story.