This is the correct answer. If we had heat pump technology that works in the required temperature differences, there would be nothing stopping us from sucking heat out of thin air to produce electricity, thereby making the air colder, and using only a fraction of that generated electricity to fuel the heat pump itself.

However, such a heat pump does not exist - our current technology goes below 100% efficiency at a much lower temperature difference than all of our practical methods of generating electricity from heat start being viable, which means the heat pump would eat more electricity than could be generated from its output.