[jameshart]

What’s the basis for this claim?

Maintaining a fixed temperature difference across a wall with a fixed thermal conductivity takes the same amount of energy no matter which side of the wall you want to keep the heat.

On the other hand, any inefficiencies in your heat transfer capability, any incoming solar radiation, and any other activity going on inside a space (like lighting, cooking or refrigeration, or just people metabolizing their breakfast) tend to add heat to it.

So maintaining a cooler temperature on the side where you’re trying to do stuff seems likely to be more inefficient than heating it.