Playing up to your opponent's level can happen in tennis too. One of the factors I think might be coming into play, especially in a sport like volleyball or tennis, is that your opponent is directly across from you and their play provides a mental model for you during the game. You can subconsciously mimic what they do, and their actions during the game act as a constant reminder for how to play well.

I noticed this snow skiing too. I had learned to ski when I was four and went multiple times a year every year, but I lived in Texas so it wasn't an everyday event. Then one mogul run I followed directly behind a more advanced skier, mimicking his moves and rhythm, and all of a sudden on that run it clicked -- my skill level shot up several folds.