A tiny clarification. I am fully aware the late night US talkshows have proper names. I know that technically it is "The Late Show with Stephen Colbert." I usually (99% of the time) shorten it to just "on Colbert" or "on Colbert's show."
No one has said anything about this to me, and I can't imagine anyone one would. But, the best journalism advisor I ever had was a stickler for proper first reference and our paper's stylebook. It drove me crazy, but instilled in me a higher level of discipline and respect for consistency. I get a little twinge every time I make a casual (on Kimmel) rather than complete (on Jimmy Kimmel Live!) first reference. And somehow, Mac would know that the complete name of the show included the exclamation point and would dink me if I left it off. But he could not cleanse me of my addiction to the parenthetical statement (but oh how he tried).