Yes, I think CBS had a promo for The Late Show with David Letterman over the 11pm/10pm Central credits leading into the Local News tease for a while. Some stations (like WGNX in the clip above) would’ve used the supplied bed/music, while others replaced it with their own theme.
Similar deal on NBC, except of course promos for The Tonight Show with Jay Leno lead into their Local News teasers.
Before Fast Action (I believe), ATN-7 Sydney used another production music track as their news theme (“Steel Town” by Roger Roger and His Orchestra (which was also being used by BTQ-7 Brisbane at some point during the late 60s/early 70s)). Along with a teletype theme (a la CBS Evening News with Walter Cronkite and several CBS O&Os at the time) for ATN 7 News during the mid-60s (followed by a “Report '66/'67” animation).
I believe Rick Wakeman’s “Overture” was used as by ATN7 Sydney as its news theme for a short period of time (October 1981-early 1984). Then they used NBC Nightly News electronic theme (sans the NBC chimes) by Joseph Paul Sicurella, Tony Smythe and Bob Christianson from mid-1984 until early 1985 when they started using Let’s All Be There as their slogan and the NBC affiliate package as its news theme.