Don't disagree, but a couple of things ...
For the record, Dixon did not "want to leave Pittsburgh." This is an exact quote to me from someone who knows Dixon very, very well ... spoke with Dixon every day (still talks to him regularly). Dixon was obviously not happy working under Barnes/Chancellor Gallagher. But Dixon did NOT expect Pitt to lower the buyout and on Sunday evening, he told his assistants he was staying. But on Monday morning, Pitt told TCU they would lower that buyout to let him go, and on Monday afternoon, Dixon was announced as TCU's new coach.
If Barnes wanted Dixon as his coach, Dixon would not have gone to TCU. But obviously, Barnes was satisfied enough to let him go.
Beyond that ... like you said ... THEN hiring Stallings was the final death penalty move to Pitt Hoops.
Personally, I'm of the belief that Barnes was simply not very impressed with Dixon and thought he could get someone more cheaply and more easily (aka Stallings) to do what Dixon did.