The previews for next episode suggest the reason why not.
As to the question of where the power is coming from and so on: obviously they could have a generator running, or the water could be gas-heated, or both. But in either case, there's the question of fuel.
It's possible to set up a remote home with an inverter, a device that takes battery power and turns it into line power. That's the industry I work in. Renewable energy could keep the batteries charged to power the inverter. A place of that size might have a creek or river with a DC microhydro turbine, which would charge the batteries 24/7. That would explain being able to run lights at all hours, electric shavers, and running water (assuming there's an electric well pump somewhere). The only thing you have to worry about is running down the batteries-- and they will
But it still doesn't explain the hot water. Electric water heaters are power HOGS and would run down the batteries pretty fast. The water would need to be heated by something else. Someone, somewhere, should have been carping about wasting some kind of fuel.
Maybe they have a solar thermal water heater?