He does say, "That price does not include windows, door, insulation or interior furnishings. In place of a brick fireplace I have recommended a recycled steel barrel stove and stove kit from Vogelzang that would be more efficient."
Those things he is excluding will easily double the price. A wood stove costs thousands, maybe hundreds used. 8 sqft of insulation is $50. Windows are $200 each. A door the same or more. And also, 10'x15' isn't really viable for a home, even for one person, much less a family that wants a shower in the bathroom.
We also have building codes now that require a functional kitchen and bathroom which add significantly to the price of a livable structure the government won't tear down.
I think bare minimum costs to build a livable structure today, would be in the $50,000 range and the mortgage on that would be $300 per month, which would fit within my proposed living stipend of $2,000 per month per family of 4.