This woman does not have to forage for tree branches because she can't afford feeding her furnace. She doesn't have a furnace in Coppell, call any real estate agent in that area. And if you do call, also ask for basements and see how many say "No, we don't have houses for sale with basements or furnaces".
Northerners are easily shocked in Texas, and lazy writers are easily tripped up.
The article may be BS, but you seem to be tripped up over the word "furnace". I have two houses in North Central Texas with central heat/AC. The heat on both are provided by gas furnaces.
Furnace An enclosed heating device powered by coal, oil, propane or natural gas.