Soon after the 'Perry Mason' episode "The Case Of The Shifty Shoe-Box" begins, young Miles is seen watching TV. The audience back in the Trueniverse can't see what's on the screen, but the voices of James Arness and Milburn Stone can be heard.
The show isn't identified as 'Gunsmoke' during that 'Perry Mason' scene, but attentive voice-over agents should be able to identify the characters as Doctor Galen Adams and Sheriff Matt Dillon.
We could always say that Miles was watching something entirely different; that Stone and Arness were playing other roles. But they're speaking lines of dialogue that should be treated as historical fact from nearly a century before.
So it's easier to splain this away as a TV show - by any name, even 'Gunsmoke' - which was recreating the lives of real-life figures of the Old West, Doc Adams and Marshall Dillon.
(Well... almost any name!)