This is a myth. Any source of heat will produce an equivalent amount of dry air, unless of course it releases combustion gases inside the house.
The cause of the dryness is outside cold air infiltrating and then being heated up, which creates very, very dry air. The difference between houses is not the source of heat, it's the amount of cold outside air that leaks in.
Heated with wood for 12 years in CO and NM. My wife used to just keep a pot of water boiling on the stove and no problem with dryness.
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.