2 shot shoot out was the cornerstone of the 'free shot'. The great players that could cut the hair off a ball (Rempe) would roll out a 70 degree lengthwise up/down table 5 rail cut and make it almost every time. Roll out made you a better player quicker and made you more aware of table speed and the free shot.
I learned to play in 1975 in the Philly area. If someone came up to you that you didn't know, we'd simply confirm the game by saying "Push-out, 2 misses BIH." That's all we needed to say. As dabarbr mentioned, if you pushed, & your opponent took it, he had to make a good hit or it was BIH.
IMO, WITHOUT QUESTION, it made for more of a shotmakers game than TX Express. You either learned the long cut and other tough shots, or you learned to hate your money! And it paid to know your opponent's strengths and weakness, far more so than Tx Ex. Exploiting weaknesses was huge strategy.