In the movie, A League of Their Own," the announcer introduces a program with "The Mutual presents..." I never head the network referred to as "The Mutual." The mic flag shows the Chicago station originating the program as WHN - at the time, it was WGN. WHN was in New York and not a Mutual affiliate at the time (the Mutual station was WOR). At the time of the film (World War II) Mutual was owned by WOR, WGN and other major affiliates. In the early 80's, WHN was a Mutual affiliate and both the station and the network were co-owned.
When I was growing up in the Detroit area, Mutual was carried by CKLW, Windsor and I thought of Mutual as a Canadian network. I though the name must have come because it carried it operated between the two countries. At the time, Mutual was broadcasting "Challenge of the Yukon" (aka "Sergeant Preston), which I also thought of as Canadian, not knowing it actually came from WXYZ in Detroit. CKLW at the time was also one of Mutual's owners. Orginally, WXYZ had been a partner in Mutual and then pulled out to join NBC (Blue Network). However, WXYZ was contractually obligated to provide "The Lone Ranger" to Mutual and for the next several years, WXYZ produced "The Lone Ranger" but Detroit listeners heard it on CKLW. Later, there was a similar situation for Sgt. Preston.