What that story also shows is that Stitt had a deep, DEEP understanding of chords and chordal relationships -- and that was the basis of his playing.
Stitt's ability to analyze the situation and call out a tune that he KNEW his "adversary" would not be able to play well indicates that Stitt's approach to music is comparable to the way an expert chess player can analyze a chess board. That is, he thought in pattern-like, even mathematical, terms. And that's (one reason) why Stitt could cut other sax players so effectively on the bandstand.
Of course, I'm not saying that Stitt was a literal mathematician. No more than I'm saying that Dexter wrote poems. They're just analogies.
EDIT:
By the way, I don't think Jim's description of Stitt as a "comfort" player is a contradiction in any way to the analogy that I'm offering. I think we're just focusing on different aspects of the same thing. For example, when we think of "comfort food," we think of things that are regular and familiar and predictable. Biscuits and gravy. Mashed potatoes. Chili. BBQ. We like these foods because we know what's coming, and we LIKE what's coming. Turning to music, the Blues is just the same, right? I, IV and V. The familiarity -- the knowing what's coming -- is what makes it feel so good. ... Well, what's more predictable than math? 2 + 2 always equals 4. That ain't ever gonna change. Of course, Stitt was operating on a MUCH higher level than that. But it was still mathematical -- regular and predictable.