This may be true for many people, but I haven't found it true for me.
My wife and I reverse the stereotype of married couples and thermostats: she was raised in an area of the world that never got below 10C in Winter, and thus no buildings ever had heat. In the Winter you just put on more clothing. I was raised near the Canadian border; so our houses were always reasonably warm. She'd prefer the thermostat at 15C. We had sort of negotiated to keep it at 19C.
When I started working from home due to the lockdown, however, I had no choice but to turn up the temperature in the room I was working in: At 19C, sitting still all day, even wearing long underwear, woolen socks, and a very warm top, my feet got cold enough to get numb, in spite of my torso being almost hot enough to sweat.
Maybe if I found the right clothing, my legs would keep my feet warm again. But the "torso warm therefore extremities warm" is definitely not true for me.
EDIT: Just to be clear, my goal was to contradict the specific claim that I quoted, not to contradict the general idea of wearing more clothes. I've tried a couple of different solutions with the equipment at hand (like hot water bottles and thick socks) and not found them effective. The heat is already controlled on a per-room basis, so an additional electric heater would probably be a lot more wasteful than just turning up the temperature by one degree. I've been looking at woolen "boot slippers" online and looser-fitting garments. I'm sure I'll find a solution -- but all of these additional measures prove that "just keep your torso warm" is not always enough.