If you research Chet's history, you'll find he WAS instructed in music theory in schooling. As a jazz musician myself, I find that looking at chord changes on a page measure by measure can seriously inhibit your improvisation. Chet (as well as myself) played from the heart with the scales and music theory learned by muscle memory. I find that Chet liked to play melodies rather than continuous bebop lines which can easily be mistaken for a lack of knowledge in music theory.
Claudio Roditi (famous Brazilian jazz trumpeter who subbed for Chet on a number of dates toward the end of Chet's career) once confirmed for me that Chet knew next to nothing about "music theory"... either that, or he never indicated that he did. In Cluadio's paraphrased words: "... he didn't know chords, but his natural ear, and his sense of timing were impeccable".
Chet Baker is, hands down, one of my favorite jazz players (and singers). His dedication to lyricism is unsurpassed.
{Lyrical intro]
Was it in Tahiti?
Were we on the nile?
Long, long ago, say an hour or so
I recall that I saw your smile
[Song]
I Remember You
You're the one
Who made my dreams
Come true
A few kisses ago
I remember you
You're the one
Who said
I love you too
Didn't you know?
I remember too
A distant bell
And stars that fell
Like rain
Out of the blue
When my life is through
And the angels ask me
To recall
The thrill of them all
When your life was through and the angels asked you to recall the thrill of them all, for sure you told them that making this fantastic music is what you remember the most of all!