Forget about Coby, lets talk hip height in general. Strength plays a big part when it comes to hip height, but we can't assume that gains in the required strength go hand in hand or is dependent on gains in the weightroom. (we know carl was not squating twice his bw).
JJ made a great point about letting the knees lead, this is something I also believe in. However, we are not talking about an athlete who is doing things right. Pushing the knee up is a corrective measure for a sprinter pushing out the back. If you are pushing out the back the knee cannot lead, your foot gets left behind(big but kick). You have to be on top of yourself if you want the knees to trully lead. When you push out the back your hip flexors are doing the work to recover the leg, not the track.
Bruny did exactly what pushing the knees up would teach a sprinter to prevent. Maybe the word "pushing" is giving the wrong idea. Some coaches use bounce up instead. The idea is to get a feeling for the force or what ever it is, that causes your knee to lead. Do some runs on a track then do some runs on the grass, you should feel a lack of spring or bounce and your knee lift should suffer when on the grass. Well the track does not absorb you forces the same way as the grass, it pushes back sending your knees up,(knee leading) hence the term pushing the knees up.
This is not something to be thinking about during a race. It is simply a "drill" to try and correct an athlete that has the problem pushing out the back. It is used much like any step over drill.
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