Actually it is not a myth. Even a modern home will draft and heating the house causes the draft to exit from the upper portion and draw in air from the lower portion. Trust me, Colorado mountain air in the winter time can be very dry.
You bet. It just doesn’t make much difference whether you heat with a wood stove or propane. Trying to heat with a fireplace will, as it sends so much air up the chimney which pulls even more air in from outside.