While your generally right, I wouldnt agree with that improved jumps wouldnt equal improved sprints times. Better jumps = better elasticity, which will = faster sprinting, although most the faster sprinting will be for acceleration.
As well, If I gave an already trained sprinter, a magic 150 pound bonus to their deep squat, with nothing else, no negatives, their sprint times would most definitely improve. How much would depend on how strong they were before it and what their weaknesses are, but times will drop.