I think the reason its never or rarely heard in a local pool room is in a local room, its usually 1 on 1 gambling. The players are usually putting up their own cash, maybe one has a backer if they are the local hot shot.
With these multi-thousand dollar action matches, of the best players in the world, the money is coming from lots of people pooling together. So the phrase in the middle makes more sense to use in these larger cases becaue in truth no single entity is putting up half the "middle" amount. Its split many ways.
Conversely, it doesn't make any sense to use the "middle" term in a local matchup of $200 sets.
That makes perfect sense. I assumed that each had a backer for the set amount. It definitely was a treat to get to watch.