Depending on the type and size of the heater relative to the area to be warmed that statement could very well be false.

I have lived in some places where turning up the heater produced much hotter air than at a lower temperature, which would heat a house much more quickly. These houses had relatively modern central air conditioning systems with electric furnaces, or really good gas furnaces.

I've also lived in places with radiators or really crappy wall mounted heaters where it wouldn't make any difference at all.