Let me throw on my AVSForum hat for a second...It's easy to confuse FM with FM. The FM being discussed here is frequency modulated, meaning that the audio was encoded into a frequency modulated signal. This did not mean that TV was in the FM (also standing for frequency modulated) band. The FM band was in the channel 6 area as correctly pointed out by Quad Linda. But what is being discussed here is that the audio was frequency modulated rather than amplitude modulated or phase modulated.
The purpose is that FM, like on your car radio, is relatively immune from noise and can go 20Hz - 18kHz (pilot gets in the way to go higher).
In the early 1980s, the FCC approved TV Stereo. In 1983-ish, I purchased a stereo TV Tuner from Radio Shack and had that hooked into my receiver. It was great compared to the normal mono sound. The first show I remember in stereo was "The Tonight Show". I also remember NBC's "Michael Nesmith in Elephant Parts" mid-summer replacement show in stereo. It was amazing! Luckily the Rochester, NY NBC affiliate was one of the first to change over to stereo, which also included a transmitter upgrade.
Now, of course, I hear a 5.1-channel show and just think it is normal. But, there was a time when getting two channel was amazing (and the world was not in black-n-white).
Tying this back into the subject matter - the Rutles "All You Need is Cash" was about 5 years too soon for stereo TV. Of course, then all of the production from the cameras, to the editing, to the mixing board to the distribution has to support stereo. That can take years by itself as companies wait for the obsolete equipment to fail before getting the replacement.