Another thing to consider is that there are delayed training affects. As Davan noted, his sprint went up AFTER he deloaded most weightlifting. If you don’t give your body time to adapt to a new strength level, you may not see any improvement. Also, if you switch exercises, say going from heavy cleans to something else, you may see sprint begin to improve in concert with some other exercise, such as bench (see Davan again). However as Davan correctly points out, the correlation with bench press was probably not causal; rather a delayed adaption to strength increases that were only realized after a taper or even deload seems more likely.
Where this gets tricky is if Davan had switched from lunges to say snatch instead of bench, would we all think that the correlation in improvement between speed and snatch would be causal? It would be hard to tell.