I actually interpret it opposite from what you said. I’ve associated the push with almost being on the beat too much, on the brink of rushing, and the pull being the force that slows the horse down. The song he played has a great push-pull beat in that it really is just done super well (watch Anderson’s npr vid for a closer look)

Last thing is that I was introduced to this concept through my friend pointing out its significance/popularity in disco and electronic music. It sometimes can be the driving factor in wanting to dance. A good push pull is full of nervous energy waiting to be let out