This is nearly a good argument for your case, it's just a bad example.
A better example is when a scratch player is against a 4-handicapper. The 4 hcp receives shots on roughly 22% of holes over the full round. At the second play-off hole he receives a shot. He has now received a shot on 5 out...
It's usually a bit more complicated than that though, and the process of letting people through usually takes more time than that.
This is because it's usually impossible to actually catch up the slower group in front, simply because you have to wait for the group in front to get out of range...