According to Miller "When I was hired to write the theme song for Frasier, I was told not to mention psychiatry, crazy people or radio, but make it germane to the show. That was a tough one, but I called my lyricist Darryl Phinnessee and he came up with the title tossed salads and scrambled eggs, which suggests things that are all mixed up. I thought of the opening line, "I hear the blues a-calling," which seemed to fit, and we put the rest of the lyric together."
Grammer was pressed into service to deliver the goods, after the idea of using Mel Torme was nixed by Angell, Casey and Lee, the show's producers. Miller adds, "When I went into the studio with Kelsey, something magical happened. He started making it something way beyond what the song really said. It was Kelsey being Frasier."
For another perspective, here is what one of the show's co-creators, David Lee, said in the book "Frasier: The Official Companion Book" by Jefferson Graham:
It's been fun watching the different theories regarding the meaning of "Tossed Salads and Scrambled Eggs" pop up over the years. I don't think "Hamlet" has been as closely scrutinized or more divergently interpreted. Here is what I (and the songwriters - and other two creators of the show) thought it meant when we decided on it.
Hey baby I hear the blues a'-callin'
(Play on words. He's got the blues and referencing that he takes phone calls.)
Tossed Salads and Scrambled Eggs
(Mixed-up people who call in.)
And maybe I seem a bit confused
Well, maybe, but I got you pegged
(The core of Frasier's character. He is a nutcase himself much of the time, but can analyze the problems of others.)
But I don't know what to do with those
Tossed Salads and Scrambled Eggs
(Except these damn callers.)
They're callin' again.