Cold weather and climates also severely reduce the viability of electric cars, not just because of the climate control needs, but because the cold weather kills the charging capacity.
And I can imagine the robustness of the climate control leave more than a little something to be desired.
I am very skeptical too....for the reasons you detailed.
I believe the 12 volt battery controls the climate control circuitry but does not run the heat pump itself. It couldn’t possibly. On a Tesla Model 3 running the A/C at max continuously takes about 60 miles off the range, or 1/4.