With a heat pump, for instance, you might be able to produce 5BTUs per watt-hour, because you're extracting heat from the environment (a very large heat source), which would be 140% efficient.
The paragraph you excerpted has your answer:
> The key to the system’s efficiency lies in the way it uses each of the multiple stages to desalinate the water. At each stage, heat released by the previous stage is harnessed instead of wasted. In this way, the team’s demonstration device can achieve an overall efficiency of 385 percent in converting the energy of sunlight into the energy of water evaporation.
You can't drink steam (and even bottling it is futile), so that heat has to go somewhere.
With counterflow systems, like ventilation systems for houses, the inlet and outlet temperatures are pretty close to each other, and the temperature on the 'inside' of the system is either much higher or much lower.
When distillation came up a month or so ago, several people pointed out that modern systems do not operate at ambient air pressure, so the temperature delta may be less than you'd imagine.
[edit: pedants gonna pedant]