As I think I mentioned earlier, the Cowboys were in Cleveland to play the Browns on Nov. 24, and the PA announcer ended up identifying the Dallas team simply as the Cowboys; the mention of the word "Dallas" caused the Cleveland fans to boo.
Side note: I think the Cowboys really became "America's team" in the era when Roger Staubach was quarterback. It used to be almost a joke at CBS (when it had the NFC) that if stuck for a nationally-televised game on Sunday, "When in doubt. give 'em Dallas." (The Cowboys didn't hurt "60 Minutes" in Dallas, either; during the fall the Cowboys and "60 Minutes" would rank 1-2 in the local ratings, before "60 Minutes hit No. 1 nationally; "Happy Days" and "Laverne & Shirley" were next, and most of the local top 10 in the late '70s consisted of ABC shows--Dallas/Ft. Worth viewers' preferences did, and I guess still do, pretty much reflect the national top 10.)
The local churches had a standing rule: if the Cowboys had a home game at 12 N (CT), the services had to end early so people could get to the stadium (or home) to watch the game; I never recall Ch. 4 blacking out a Cowboys game.
Ch. 4, now a Fox o&o, still has the Cowboys; I suppose CBS o&o KTVT/11 has the Houston Texans.