Many years ago I thought I had invented a method to efficiently distill a continuous flow of water.There's absolutely no magic or mystery here -- they guy simply makes a misleading statement by using the phrase "your drink" and "my drink" in an ambiguous way. He leads people into thinking that fluid from the cold source comes out hotter than the hot source, and, conversely, that the fluid from the hot source comes out colder than the cold source. That's not the case, as everything he does shows. The fluid from the cold source simply comes out hotter than the fluid from the hot source comes out. But so what? The limiting factor isn't the point at which the two fluids come out -- they aren't in thermal contact there. The cold fluid is in thermal contact with the hot source at the point it comes out and the hot fluid is in thermal contact with the cold source. So the limits are that the temperatures swap. Imagine just taking the fluid from the cold source and sending it through a coil of copper tube emersed in the hot liquid and doing the same with the hot liquid sending it through a coil in the cold water. The you would expect the fluid coming out of each tube to approach the temperature of the other source.
It turned out I had "invented" exactly this (using latent heat from condensation to preheat the incoming cold water).
Counterflow heat exchangers are used in desalination plants and many other industries to capture what would otherwise be waste heat.