Steve Rannazzisi Comedy Central Airs Show Despite 9/11 Lie

9/20/2015 6:57 AM PDT

Steve Rannazzisi got a slice of good news in the wake of his 9/11 lie admission ... Comedy Central aired his special.

The network hedged after Steve disclosed he was not in one of the twin towers during the attack ... a story he propagated in vivid detail for years.

The special -- "Breaking Dad" -- aired Saturday night.

"The League" star wasn't as lucky with his lucrative Buffalo Wild Wings commercial, which was yanked off the air after he fessed up.