MOO -- I'm guessing that, assuming the firewood story is even correct, he would have been gathering kindling size sticks for a rainy-day ambience fire, not for regular home heating.
People who regularly heat with wood buy their firewood by the cord or go up to the woods to cut their own by the truckload. Not scrounge it each day.
If there was a cord of wood stacked in the empty lot against the outside of his fence, his "throwing wood over the fence" phrasing would make more sense to me.
Incidentally, an open fireplace like that shown in the zillow photo of their house, is really more of an ambience thing, "sit in front of a crackling fire on a rainy day", but it generally loses more heat up the chimney than it puts out into the house, so this would not be a good way to heat a home on a regular basis.
MOO