Where did Gene Roddenberry get the idea for the Star Trek Theme?

I was over at IMDB a little while ago and noticed that someone else had figured out why "Daisy" was used as the song that the computer, HAL, sang in 2001: A Space Odyssey. I had been aware of this information for several years but never thought to blog about it before.
Then I remembered a video I put together last year. It explains where I believe that Gene Roddenberry came up with the idea for the opening of his Star Trek Series. It's from the Outer Limits episode that starred William Shatner entitled: "Cold Hands, Warm Heart" (1964)

So I include the mashup here and see if you don't agree.

Please leave any comments about this observation below.